Can an iMac (M1) read an HDMI (out) signal via the Thunderbolt 4 (in) port using an HDMI to USB-C cable?

Generally speaking, given an HDMI out signal connected to the computer through an HDMI to USB-C adapter, is there any way to read the signal that the Mac receives and display it on the computer screen?

Just to be clear, I am not asking how to get a signal from the thunderbolt 4 (out) to an HDMI (in), I am asking exactly the opposite, how to get a signal from an HDMI (out) to a thunderbolt 4 (in).

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Specifically, I am trying to salvage old cassettes from twenty years ago, and let me tell you it has been a nightmare. Nothing reads MiniDV anymore, so I had to find an old handycam, which broke down, I found another one, which did not have the right cables, I bought the cables, the encoding was wrong, I fixed the encoding, the tray got stuck, went to repair, they cannot obtain replacement parts. Iterate over a few more handycams, and I now have:

1. something that reads the cassettes, (a working handycam)
2. composite AV cables (red, white and yellow) that plug to the handycam at a 4 pin FireWire (or “i•Link”) connector,
3. a composite AV output which (Hurray!) displays correctly on a regular flat screen television,
4. a USB powered AV to HDMI converter which, you guessed it, outputs a valid HDMI signal and, finally,
5. an HDMI to USB-C cable which I can plug into the Thunderbolt 4 ports of the M1 iMac.

I was under the impression that all I needed was open iMovie and import the signal, as if it were a mere FireWire signal, but somehow HDMI plays hide and seek. So really an alternative question is:

How in the world am I supposed to feed the output of the handycam (which reads the MiniDV tapes of two decades ago) into the computer (from this century) so that I may compile it into something a little more… future proof? (so that my grandchildren may enjoy the glory of shaky 720p footage with the colours smeared all over the place)

I've already spent more money on this than I am willing to admit, but here is a short list of solutions I have encountered which will not work in this case:

1. no cassette scanning services exist anywhere near me,
2. no FireWire are still being sold, specifically the 4 pin to 4 pin I would need to connect the handycam directly to the Thunderbolt 4 port via a FireWire to USB-C connector (that is, neither the 4 pin to 4 pin nor the 4 pin to USB-C are available),
3. plug and play AV capture gadgets have not worked so far and are mainly advertised as only compatible with Windows anyway,
4. the television fried (as in overheat) every external memory I plugged into it, refuses to capture a composite AV or HDMI signal, only captures TV channels and when it does it formats the whole disc into something unreadable on anything other than the very same television (fine with me for proprietary content, but a little brutal for my intimate memories. No luck there)
5. handycam distributors (I will not name names) have withdrawn all software support, could not find any drivers, such that even if I somehow managed to connect the handycam to the computer (even a Linux) cam and computer would never be able to talk to each other.

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In short, here is my setup:

MiniDV -> Handycam -> FireWire to composite AV cable -> USB powered Mini AV2HDMI ->HDMI to USB-C cable -> Thunderbolt port of the iMac (-> some software that would pick up the signal and display what I see when I plug the same setup into a television, and hopefully in such a way that my Mac can record the feed and save it for posterity as mp4 or m4v)

I am a little disappointed to discover at the last minute that the Thunderbolt 4 advertised as “this port that does everything” and which is technically the same kind of connector than a vulgar HDMI is refusing to play nice and at least prompt a “what do you want to do?” when connecting the HDMI out to USB-C cable, when iMacs from 2014 could readily be used as displays, welcoming an HDMI signal from the same Thunderbolt ports. Is the Mac able to see the HDMI signal and designed to ignore it?

Some of the tapes are showing signs of decay, I would really hope to be able to salvage the footage before it scrambles away. Any suggestions are very welcome. (I guess I'll give up, buy a tripod, and plain record the television with a smartphone. But I mean, how do professionals do it? Don't they have to handle cassettes or HDMI signals every now and then?)

Thanks to all.

Best regards,

Matt