[TASK] Avoid misusing element browser for link handler concerns

This resolves a mixup in ext:recordlist:

The "Browser" classes are the "element browser" modals, used
when adding FAL images to records and when adding relations
for type="group".

The "LinkHandler" classes are a distinct construct used to
create the "t3://" syntax when linking record fields and
RTE text to a page, telephone, external URL and so on. They
are rendered as single tabs in the link handler modal.

Class LinkHandler/RecordLinkHandler allows linking to arbitrary
records. Typical example is linking to single ext:news records,
which can be configured using PageTsConfig TCEMAIN.linkHandler.

Class LinkHandler/RecordLinkHandler misuses the element browser
abstraction to list records. This materializes in class
Browser/RecordBrowser, which is not used as element browser as
such, but is just a client class of LinkHandler/RecordLinkHandler.
The two class namespaces however shouldn't interfere with
each other.

The patch resolves this by moving the code from
Browser/RecordBrowser into LinkHandler/RecordLinkHandler and
streamlining it to what is really needed. A series of changed
and added comments should improve the overall constructs
along the way.

Resolves: #97957
Related: #66373
Related: #97188
Related: #96639
Releases: main
Change-Id: I3028ce439e6ae68c4ed34c0c560b4980dad6ac29
Reviewed-on: https://review.typo3.org/c/Packages/TYPO3.CMS/+/75205


Tested-by: Andreas Fernandez <a.fernandez@scripting-base.de>
Tested-by: core-ci <typo3@b13.com>
Tested-by: Stefan Bürk <stefan@buerk.tech>
Tested-by: Christian Kuhn <lolli@schwarzbu.ch>
Reviewed-by: Andreas Fernandez <a.fernandez@scripting-base.de>
Reviewed-by: Stefan Bürk <stefan@buerk.tech>
Reviewed-by: Christian Kuhn <lolli@schwarzbu.ch>