SUMMARY
Kate's LSP Client plugin matches LSP servers only on a file's Highlighting mode, which requires a KSyntaxHighlighting .xml definition for the language. LSP has the ability to provide syntax highlighting itself since 3.16, which Kate has supported since 21.08.0. If a language or filetype does not have a matching definition in KSyntaxHightlighting, you cannot use LSP.

To easily support any language with an LSP server, the LSP client plugin should expose a few options for matching, not just the file's Highlighting mode (highlightingModeRegex).

Kate file Modes—which are easy to author in the Settings dialog—are a good choice. Alternatively, LSP Client could match against file extensions directly.

SOFTWARE/OS VERSIONS
Linux/KDE Plasma: KDE neon 5.23 user edition
KDE Plasma Version: 5.23.4
KDE Frameworks Version: 5.89.0
Qt Version: 5.15.3

ADDITIONAL INFORMATION

(This is similar to Bug 447172, however that bug was unclear and messy)