[TASK] Use native objects in `@typo3/core/ajax/ajax-request`

The module `@typo3/core/ajax/ajax-request` previously had a lot of
string-based mambo jambo when composing URLs and query strings.

The API is now streamlined to use `URL` and its included `searchParams`
property to build URLs, removing the need to compose URLs manually.

Resolves: #101969
Releases: main
Change-Id: I40c73531c86d828fb298f5d6ae1a0bb9030c23cf
Reviewed-on: https://review.typo3.org/c/Packages/TYPO3.CMS/+/81098


Tested-by: Andreas Fernandez <a.fernandez@scripting-base.de>
Reviewed-by: Andreas Nedbal <andy@pixelde.su>
Tested-by: Stefan Bürk <stefan@buerk.tech>
Tested-by: Andreas Nedbal <andy@pixelde.su>
Reviewed-by: Stefan Bürk <stefan@buerk.tech>
Reviewed-by: Andreas Fernandez <a.fernandez@scripting-base.de>
Tested-by: core-ci <typo3@b13.com>