It's been niggling, but I still don't have a solution to your problem as stated. I think it's to do with the way that Windows handles the clipboard, and whether target applications "know" to handle incoming clips as plain text or HTML.
I would have liked a similar system where I could copy from a Web page, and have the HTML code as such pasted into a plain text editor. Many editors can strip HTML, some can do it while preserving links, which would give something similar to what you want. Still more actions than ideal. It looks like Firefox extension
Extended Copy Menu may be useful:
Provides the option to copy selection as plain text or html.
It adds a "Copy As Html" and "Copy As Plain Text" to the context (right-click) menu. It is useful if you want to copy the text or underlying html from a web page into documents, posts or other applications.
The difference between plain Ctrl+C and Extended Copy Menu on the current DC Forum Home Page is as follows.
Plain Ctrl+C:[General Software Discussion] Re: SrtRetime 1.1.0.0 MilesAhead Today at 03:59:46 PM
[Soap Box] FBI caught on camera 'returning' a server they confinscated. SeraphimLabs Today at 03:45:02 PM
[Soap Box] Doconian International Party: Manifesto Stephen66515 Today at 03:01:42 PM
Extended Copy Menu "Copy As Html":
<tr><td class="smalltext" align="right" nowrap="nowrap" valign="top">[<a href="https://www.donation.../index.php?board=6.0">General Software Discussion</a>]</td>
<td class="orangesmall" valign="top"><a href="https://www.donation...;topicseen#msg288198">Re: SrtRetime 1.1.0.0</a></td>
<td class="smalltext" valign="top"> <a href="https://www.donation...ion=profile;u=185796">MilesAhead</a> </td>
<td class="smalltext" align="right" nowrap="nowrap" valign="top"><b>Today</b> at 03:59:46 PM</td>
</tr>
<tr>
<td class="smalltext" align="right" nowrap="nowrap" valign="top">[<a href="https://www.donation...ndex.php?board=311.0">Soap Box</a>]</td>
<td class="orangesmall" valign="top"><a href="https://www.donation...;topicseen#msg288197">FBI caught on camera 'returning' a server they confinscated. </a></td>
<td class="smalltext" valign="top"> <a href="https://www.donation...ion=profile;u=372590">SeraphimLabs</a> </td>
<td class="smalltext" align="right" nowrap="nowrap" valign="top"><b>Today</b> at 03:45:02 PM</td>
</tr>
<tr>
<td class="smalltext" align="right" nowrap="nowrap" valign="top">[<a href="https://www.donation...ndex.php?board=311.0">Soap Box</a>]</td>
<td class="orangesmall" valign="top"><a href="https://www.donation...;topicseen#msg288196">Doconian International Party: Manifesto</a></td>
<td class="smalltext" valign="top"> <a href="https://www.donation...ion=profile;u=254145">Stephen66515</a> </td>
<td class="smalltext" align="right" nowrap="nowrap" valign="top"><b>Today</b> at 03:01:42 PM</td></tr>
as pasted into Notetab Pro. Using NTP's "Strip HTML Tags, Preserve URLs" feature on that, wrapped to fit on screen, gives:
[<https://www.donationcoder.com/forum/index.php?board=6.0>General Software Discussion]
<https://www.donationcoder.com/forum/index.php?topic=30963.msg288198
;topicseen#msg288198>Re: SrtRetime 1.1.0.0
<https://www.donationcoder.com/forum/index.php?action=profile;u=185796>MilesAhead
Today at 03:59:46 PM
[<https://www.donationcoder.com/forum/index.php?board=311.0>Soap Box]
<https://www.donationcoder.com/forum/index.php?topic=30971.msg288197
;topicseen#msg288197>FBI caught on camera 'returning' a server they confinscated.
<https://www.donationcoder.com/forum/index.php?action=profile;u=372590>SeraphimLabs
Today at 03:45:02 PM
[<https://www.donationcoder.com/forum/index.php?board=311.0>Soap Box]
<https://www.donationcoder.com/forum/index.php?topic=30970.msg288196
;topicseen#msg288196>Doconian International Party: Manifesto
<https://www.donationcoder.com/forum/index.php?action=profile;u=254145>Stephen66515
Today at 03:01:42 PM
CHS sees Ctrl+C and Extended Copy Menu clips as separate entities, as witness the screenshot. But, of course, this only works for Firefox, and Extended Copy Menu is quite old (I'm still using an old copy of FF). I presume it should be possible to used editor macros to convert URLs into BBcode or whatever.