I’m getting some wiring run about the same distance (to my attic, fished up a wall, with moderately poor access) for non-EV purposes next week and the quote was a few hundred dollars.
running to another room will be done usually (at least in usa) through attic or crawlspace. i got it done a few months ago to have dedicated 20A circuit (for my rack) in my work room. cost was around 300-400 as well
Honestly I wouldn't expect to pay less than $1000 for the job w/o any markups.
I've gotten multiple quotes on running the 240v line, the labor breakdown was always over $400 alone. Just having someone show up to do a job is going to be almost $200 before any work is done.
When I got quotes from unlicensed people, those came in around $1000 even.
another thing, which is good long term is to a find a local electrician (plumber, etc) who doesn't charge service calls and have reasonable pricing.
no idea about handyman pricing. never used any. for electrical/water/roofing i prefer somebody who is licensed/insured/bonded/etc
I got a quote for over 2 thousand to run a 24v line literally 9 feet from my electrical panel across my garage to put a EV charger in.
Opening up an actual wall and running it to another room? I can only imagine the insane quotes that'd get.