you can absolutely do it yourself. be prepared and get the right tools, look up many many guides and videos before you start, but I honestly think it's doable for someone whose never opened a phone. those batteries are an absolute pain in the ass to remove, but as long as it's discharged below 20% you really don't have to worry about it it catching fire or anything catastrophic like you're lead to believe (just be careful ofc and wear PPE)
Been a while since I looked, but last time I checked around me, the starting price for any work like that was like $200 (maybe it was less?). Not exactly worth it for a $300 phone that's already aging unless you need data off it or something. Granted, YMMV with pricing.
battery replacements usually run around 60-90 at my shop depending on the device, if I ever walked in to a shop and heard 200$ I'd walk tf out that's insane pricing.