Hi all!

TL;DR I am considering purchasing a used camera to replace mind. I would like it to be quite compact, not too expensive (600$ budget), good at higher ISO levels, with good connectivity options and would be intrigued to try out full-frame.

The Background: I’m considering upgrading my Canon 1300D, which I’ve owned since 2018, to a newer camera. The main limitation I’m experiencing is poor image quality at higher ISO levels; the noise becomes noticeable even at ISO 800.

My Gear: Currently, I use the Canon nifty fifty, the EFS 55-250mm f/4-5.6, and a Tokina 12-28mm f/4. With this setup, I’ve traveled to Thailand, Iceland, Cuba and it worked pretty well so far (not amazingly but I am satisfied)

Investing in Education: In the short term, I’ve decided to spend money on an advanced photography class which starts tomorrow. I think this is probably the best investment I could make as a photographer. However, I’m torn between upgrading my camera or reshuffling my lenses (possibly trading the Tokina for a pancake lens for improved portability).

New Camera Goals: I’d like to move to a faster camera and I’m also eager to experience shooting with a full-frame model.

The Big Question: Given the above, and with a budget of around $600, what would you suggest? Are there any compact cameras that perform well at higher ISO levels and come with good connectivity options (wifi, bluetooth, and such)?
I am also open to switch to different brands, and could consider mirrorless.