* test/lisp/progmodes/lua-ts-mode-tests.el (lua-ts-test-font-lock):
Add ert-font-lock tests.
(lua-ts-mode-test-indentation):
(lua-ts-test-indentation):
(lua-ts-mode-test-movement):
(lua-ts-test-movement): Rename for consistency.
* test/lisp/progmodes/lua-ts-mode-resources/font-lock.lua: New
file.

* lisp/progmodes/lua-ts-mode.el (lua-ts-mode): Improve movement.
(lua-ts--simple-indent-rules): Improve indentation rules.
(lua-ts-mode-map): Add key bindings and menus.
(lua-ts-mode-hook): Make hook available in Customize.
(lua-ts-inferior-history, lua-ts-inferior--write-history): Add option
to read/write an input history file.
(lua-ts-inferior-lua, lua-ts-send-buffer, lua-ts-send-file)
(lua-ts-send-region, lua-ts-inferior-prompt)
(lua-ts-inferior-prompt-continue): Support for sending buffer,
file or region to the inferior process.
(lua-ts-show-process-buffer, lua-ts-hide-process-buffer)
(lua-ts-kill-process): New functions.
(lua-ts-inferior-prompt-regexp): Remove option.
* test/lisp/progmodes/lua-ts-mode-resources/indent.erts:
* test/lisp/progmodes/lua-ts-mode-resources/movement.erts: Add
tests.

* lisp/progmodes/lua-ts-mode.el:
* test/lisp/progmodes/lua-ts-mode-resources/indent.erts:
* test/lisp/progmodes/lua-ts-mode-tests.el: New files.
* etc/NEWS: Mention the new mode.
* lisp/progmodes/eglot.el (eglot-server-programs):
* lisp/progmodes/hideshow.el (hs-special-modes-alist):
Support 'lua-ts-mode'.
* admin/notes/tree-sitter/build-module/batch.sh:
* admin/notes/tree-sitter/build-module/build.sh: Add Lua.
* test/infra/Dockerfile.emba:
* test/infra/test-jobs.yml: Include lua-ts-mode tests.