I'd go with a bowtie joint or similar.
Filling the crack is one thing, but I'm not sure I'd be enough to prevent further splitting in the way a bowtie joint would.

Adding another view of the damage.

One thing to think about is expansion. If that gap closes up when it gets humid and opens again when it dries out filling the gap will just cause new splits when the wood expands again.

You could fill in the larger areas with wood shims and then finish off the face with wood putty, basically wood glue with sawdust mixed in. You can buy it premade. It stains more like wood than glue does.

No advice beyond what others have given, but good luck, and I'd enjoy Wing Chun related content if you want to post that too!

not an expert, but your plan sounds far from stupid.

I would leave it alone. Given the age of the wood it will likely not crack any further. It has already dried as much as it can.

You can mix wood glue with sawdust and pack it in the cracks

For such a narrrow crack, getting enough epoxy into the space to restore structural strength will be tricky. I've had good success with fine sawdust 'petrified' in place with cyanoacrylate (CA) glue. Practice on a test piece to optimize colour. A museum conservator would probably not disguise the repair, but if you are trying to do that, consider refinishing the whole piece. Changing moisture conditions, as already pointed out, will stress any repair but given the piece's age, maintaining humidity within normal indoor conditions will minimize any movement.

What about wrapping it with cord/rope? That would be reversible, and keep a similar aesthetic