How long should the mounting screws be?

Long enough to bite properly, short enough to never bottom out. Both failures are real: too short strips the insert under load, too long can crack the case or press on the panel from inside.

The rule the number comes from

Length = bracket + spacers + engagement. Engagement into the TV's insert should be at least the screw's own diameter — 4 mm for M4, 6 mm for M6, 8 mm for M8 — and must never exceed the maximum depth in the manual, because behind the insert there is a panel, not more metal. When the calculator can't find a standard length inside that window, it says so rather than rounding past a limit: add a washer under the head to shorten the effective length, or use the exact screw the manual specifies.

Answers to the questions around this one

• Do TVs come with mounting screws? Almost never — the threaded holes ship empty or holding stand bolts. Mounts are what include the screw assortment.
• The screw stopped turning halfway in. Stop. Either the length is past the insert's depth or the thread is wrong. Forcing it is how panels crack.
• Snug, not torqued. Hand tools, firm and seated. A power driver in a metal insert set into plastic is asking for a stripped thread.
• Washers are legitimate tools. One washer shortens effective length about a millimeter and spreads the head's load. The kit includes them for a reason.

The thread and stated screw length for your exact TV may already be on its spec page. More tools: the mounting height calculator and the fireplace check.