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Just like in web browsers: add current open file to a list so I'm able to re-open it any time again, unbound to my "recently opened files" list. Preferably not limited in an arbitrary way (i.e. only up to 64 entries), and I'm fine if it can only be managed (other captions or removing entries) by editing a text file.

Low priority - it just occures from time to time that a favorite list would have been handy.

Choose a file to hold your bookmarks, say C:\path\to\bookmarks.

Create a TextPad "DOS" tool:
Configuration | Preferences | Tool | Add | DOS Command...

Command: cmd
Parameters: type C:\path\to\bookmarks

Regular expression to match output:
^(.+?)(?: *\((\d+)(?:,(\d+))?\))?$
(or whatever you prefer)

File: 1 Line: 2 Column: 3

Include
C:\path\to\bookmarks
in itself.

You can specify a line number:
C:\path\to\bookmarks (42)
and a column number:
C:\path\to\bookmarks (42,21)

Assign a convenient shortcut key to this tool. (I use <Ctrl+Shift+F1>.)

Never thought about executing a process. It's not exactly what I'm looking for but a approach worth investigating - most likely I'll add another execution to append a line to the existing bookmarks file...