Is HDMI port vulnerable to lightning

Any electronic component ca. Be damaged by electrical surges like an electrical strike

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gains:

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Vulnerability to lightning

Any electrical connection including networking can be a conduit for a lightning strike. Unless you have an extraordinarily expensive surge protector, likely installed at your circuit breaker panel, you don’t have lightning strike protection there either

You can try plugging it into another HDMI port to see if just the port was fried, you can try it on another TV, but I would expect that it’s dead

With a lightning strike the spike could come through any of the connected ports, be it the power supply, the hdmi port or the ethernet port if you are wired.

As stated above your best bet might be to claim it on your homeowners or renters insurance.

Even if it was on a surge protector, many don't trip fast enough to deal with strikes, but some do have property protection if they fail. So if your equipment was on one you might wanna check.

Yes, lightning could damage some of internal circuits that's responsible for hdmi