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What is this C#/.net5 notation called with a colon in a interpolated string?

I came across some notation in an interpolated string currentDate:d in the Microsoft documentation but they do not elaborate on how it works or what it is called, so I don't know how to look it up further. It appears to deconstruct a DateTime and get the date and time specifically, and only seems to work in the interpolated string; I can't use the same trick to pull the time out into a variable. I'm wondering if I can use that notation for other objects and how it works.
var currentDate = DateTime.Now;
var time = currentDate:t; // this throws error
Console.WriteLine($"{Environment.NewLine}It is currently {currentDate:d} at {currentDate:t}!");
outputs:
It is currently 2021-10-31 at 10:41 AM!
MS docs source: https://learn.microsoft.com/en-us/dotnet/core/tutorials/with-visual-studio-code?pivots=dotnet-5-0
I can't think of a better way to ask this question, so would appreciate a hint.

It is explained in the docs that you linked. It says:
The dollar sign ($) in front of a string lets you put expressions such as variable names in curly braces in the string. The expression value is inserted into the string in place of the expression. This syntax is referred to as interpolated strings.
The link there takes you to the page "$ - string interpolation - C# reference", which has a section named "Structure of an interpolated string" that says this:
The structure of an item with an interpolation expression is as follows:
{<interpolationExpression>[,<alignment>][:<formatString>]}
[...]
formatString: A format string that is supported by the type of the expression result. For more information, see Format String Component.
The link "Format String Component" then gives you all the info you need:
The optional formatString component is a format string that is appropriate for the type of object being formatted. Specify a standard or custom numeric format string if the corresponding object is a numeric value, a standard or custom date and time format string if the corresponding object is a DateTime object, or an enumeration format string if the corresponding object is an enumeration value.
[...]
Date and time types: Standard Date and Time Format Strings / Custom Date and Time Format Strings
The linked page "Standard Date and Time Format Strings" explains d as follows:
Format Specifier
Description
Examples
d
Short date pattern. - More information: The short date ("d") format specifier
2009-06-15T13:45:30 -> 6/15/2009 (en-US) [...]
This already explains it in short, but the link provided in the table leads to an even more detailed explanation.
This also shows an example of how to use such a format string outside of an interpolated string, using the ToString method:
DateTime date1 = new DateTime(2008, 4, 10);
Console.WriteLine(date1.ToString("d",
DateTimeFormatInfo.InvariantInfo)); // Displays 04/10/2008
Console.WriteLine(date1.ToString("d",
CultureInfo.CreateSpecificCulture("en-US"))); // Displays 4/10/2008
Console.WriteLine(date1.ToString("d",
CultureInfo.CreateSpecificCulture("en-NZ"))); // Displays 10/04/2008
Console.WriteLine(date1.ToString("d",
CultureInfo.CreateSpecificCulture("de-DE"))); // Displays 10.04.2008

It's just some of the standard date and time format specifiers.
"d" is the short date format specifier, "t" is the short time format specifier.
More info can be found at Standard date and time format strings on MSDocs.
Aside: You could have achieved this without string interpolation as well:
Console.WriteLine("It is currently {0:d} at {0:t}!", currentDate);

DateTime Format provider for filepath

I have a file-path that's been created from DateTime stamp:
"C:\\Logs\\Tests\\2015\\Mar\\24\\13_32_09\"
Now I am trying to convert my file-path back to DateTime object.
With Regex I can easily remove "C:\\Logs\\Tests\", but now I am assume I need to provide implementation of IFormtProvider to convert 2015\\Mar\\24\\13_32_09\ into a DateTime object, but I haven't come along any similar example of how that's usually done.
Any example, may not be particular solution to my answer, would be helpful.
Thanks

You can use DateTime.ParseExact like:
DateTime dt = DateTime.ParseExact("2015\\Mar\\24\\13_32_09\\",
#"yyyy\\MMM\\dd\\HH_mm_ss\\",
CultureInfo.InvariantCulture);

No, you don't need to create an IFormatProvider at all. The invariant culture is fine for this (assuming the month name is always in English). You can just use DateTime.ParseExact, passing in the appropriate custom format string (quoting the literal characters, either with apostrophes around them or backslashes before them):
var dateTime = DateTime.ParseExact(
text,
#"yyyy'\'MMM'\'dd'\'HH'_'mm'_'ss'\'",
CultureInfo.InvariantCulture);
Note that this assumes the path really does use backslashes... it won't work on Unix as-is. (You might want to canonicalize the directory separators first.)

DateTime.ToString() not working as expected

In the screenshot DateTime.ToString() method is being called but the date is not getting formatted in expected format (as seen in Quick Watch widnow). Is something wrong ?

You are using / as separator in your ToString format. But your current culture seems to has - as date separator. That is why you see the difference. You can pass CultureInfo.InvariantCulture with ToString.
Like:
DateTimeObject.ToString("MM/dd/yyy HHmmss", CultureInfo.InvariantCulture)

DateTime.ToString replaces / with the current date separator and : with the current time separator. You're passing in the format yourself, and it does not match what's in the Region settings.
To use the Region settings, use ToShortDateString() and ToShortTimeString().

You can use this:
DateTime.now.ToString("yyyyMMddHHmmss");
or
DateTime.now.ToString("mm-dd-yyyy");

Parse Datetime string

I'm trying to convert the following string to datetime. I've searched high and low and can't find the exact formats string and I don't want to resort to parsing it manually.
var dateString = "20110828T134108+0100";
All my attempts fail with FormatException.

Have you tried this?
var date = DateTime.ParseExact( dateString
,"yyyyMMdd\THHmmsszzz"
,CultureInfo.InvariantCulture
);
From MSDN:
If format is a custom format pattern that does not include date or
time separators (such as "yyyyMMdd HHmm"), use the invariant culture
for the provider parameter and the widest form of each custom format
specifier. For example, if you want to specify hours in the format
pattern, specify the wider form, "HH", instead of the narrower form,
"H".

The documentation on the format string is here: http://msdn.microsoft.com/en-us/library/8kb3ddd4.aspx
That should get you started. :)

try this format: "yyyyMMdd'T'HHmmss"

Have you tried this:
DateTime.ParseExact("20110828T134108+0100", "yyyyMMdd'T'HHmmsszzzz", CultureInfo.InvariantCulture);

Convert String to Datetime C#

I have a string value which is a datetime : "20100825161500" and I want to convert this to a System Datetime. I have tried Convert.ToDateTime and DateTime.Parse and these do not work.

You can use DateTime.ParseExact to pass the format you need.
Here is an example:
var parsed = DateTime.ParseExact("20100825161500","yyyyMMddHHmmss", null);
Possible format values are listed at
Standard Date and Time Format Strings and Custom Date and Time Format Strings

Try to use something like this
Datetime D = DateTime.ParseExact("20100825161500","yyyymmdd...",null)
here you have a link about how to make you "format" string

Because this string hasn't a format recognized by these 2 functions.
DateTime.Parse and Convert.ToDateTime require your string to be correctly formatted :
http://msdn.microsoft.com/en-us/library/1k1skd40.aspx
http://msdn.microsoft.com/en-us/library/xhz1w05e.aspx
You will have to write your custom parser for this kind of conversion