Tenuifolia growing over sides of pot
 

I was gifted a maxillaria tenuifolia (no prior experience) and it’s so full I’ve been afraid to repot. But it’s growing over the sides of its pot, and it’s so tight I can hardly feel the soil (or even get a bamboo skewer) in to see whether or how dry/moist it is!
My question is whether to repot, should I use ring support to keep it vertical, type of pot (indoors), and media.

Welcome!

I would remove it from that pot, gently shake off only loose medium, set in a pot that fits, and backfill with new medium. Keep in mind that these like a lot of water.

You could just cut the pot and drop the plant into something a bit larger (not disturbing roots... this species really hates that) It blooms best when it is climbing out of the pot, eventually the pot becomes irrelevant. (The root system runs the length of the growths... don't ever remove those brown sheaths)

Take a look at this one, shown by a fellow orchid club member:
Southern California Orchid Species Society6-2019