The pattern of "sometimes boots after many hard restarts" and "boots semi-normally after reconnecting to TV" strongly suggests intermittent hardware failure rather than pure software corruption — a software corruption issue would not fluctuate based on being plugged into an external display or on how many times you power cycle it.
Step 1 — Force restart and try to reach WinRE
Hold the power button ~20 seconds to force a shutdown, then power on. If it fails to boot twice in a row, Windows should automatically drop into Windows Recovery Environment (WinRE).
Step 2 — From WinRE, go straight to the command-line repair (skip the black-screen shortcuts)
Choose option → Troubleshoot → Advanced options → Command Prompt. If prompted, enter your BitLocker recovery key. Then run, in order:
bootrec /scanos
bootrec /rebuildbcd
bootrec /fixmbr
bootrec /fixboot
This is safe — it only rewrites boot records, not your files. Skip the Win+Ctrl+Shift+B / Win+P display shortcuts entirely; those only work once Windows has already loaded in the background, and your black screen happens before that point, so they won't do anything here.
Step 3 — If Windows starts after that
Immediately finish your backup if you haven't already, then install the latest Surface and Windows updates.
Step 4 — If it still won't boot, use a USB recovery drive / Surface recovery image
Shut down, insert the USB recovery drive, hold volume-down while pressing power, release volume-down when the Surface logo appears. Note: this step can wipe the drive, so only do it after Step 0 backup is done (or accept that you may not get another backup chance).
Step 5 — If BitLocker keeps reappearing after firmware-related changes
Boot to Surface UEFI → Security → Change Configuration under Secure Boot → Microsoft Only → OK → Exit/Restart. If it still won't boot even with the correct recovery key, use the BitLocker key together with the Surface recovery image on USB.
Step 6 — Stop here and go to service
Given all of the following together — two months of intermittent failure, worsening boot success rate, the SrtTrail.txt automatic-repair failure, and especially the scrambled clock/PIN digits on the lock screen — this combination points to a hardware fault (most likely GPU/display controller or a failing storage module), not something any software repair step will fix. That visual corruption symptom is the deciding factor: no bootrec command or recovery image fixes corrupted on-screen rendering. If Steps 1–5 don't produce a stable boot, don't keep cycling through more troubleshooting — go directly to Microsoft Support / an authorized Surface service center for hardware diagnostics (SMART data, GPU/display controller check) rather than risking your last usable boot window on more recovery attempts.