How long does a steam refund typically take?

I thought this would be an automated process.

not entirely. while steam does auto approve refunds for games that are both owned less than 14 days & played less than 2 hours (not sure if this part is automated or if they train staff to just glance at the playtime & click refund in their ticket system), they still have a refund department to vet & process refunds that fall outside of that category. they'll send you an email if what you're refunding doesn't fit the criteria for automatic approval:

Valve will, upon request via help.steampowered.com, issue a refund for any title that is requested within 14 days of purchase and has been played for less than 2 hours (this includes online, offline and shared library playtime). Even if you fall outside of the refund rules we've described, you can submit a request and we'll take a look at it.

if you played the game for over 2 hours, even if it's just by one minute, your request is gonna be in limbo for a while until a support team member gets to it. i've had it happen a few times over the years & in my experience it takes anywhere from like 1 or 2 days to as many as 5, depending on how busy it is (steam sales seem to slow them down). i've also heard from some on the steam community that even when a refund is auto approved it can sometimes still get stuck in the system for a few days.