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Unfortunately JWST won’t come close to being able to resolve Sgr A*. They measured its diameter in micro-arcseconds, whereas JWST’s limiting resolution will be measured in 10s-100s of milli-arcseconds.

And would it even be able to see past the dust clouds and stars and stuff in front of it?

I mean if they could, they could do another longer term observation like from that clip where you can see stars swishing around it.

JWST is an infrared scope pretty much specifically so it can see through dust clouds.

JWST is not large enough to have that kind of resolution. EHT collaboration has effective lens size comparable to the diameter of the earth.

Yes, IR better penetrates the dust cloud hiding Sgr A*, so here's hoping.

The EHT reveals the black hole shadow of about 50 micro-arcseconds [1], while JWST has resolution of about 0.1 arcsec [2], thus resolution of JWST is more than 2000 worse.

It is physically impossible (regardless of the exposure time) for JWST to resolve Sgr A*.

1. https://physicsworld.com/wp-content/uploads/2022/05/First-SG...

2. https://webb.nasa.gov/content/about/faqs/facts.html

Interesting, thank you.