Bathtub drain has hole in it and the pop up drain is also stuck
At my house a slow bathtub drain is from my wife and granddaughters showering. the pop-up assembly usually unscrews if it already has a hole and you can’t unscrew by hand get a pair of pliers and unscrew it if it is still draining slow. unscrew the drain nut a basin wrench is the correct tool but I use 3 screwdrivers all the time.
Hold 2 screwdrivers in the drain cross bars and the 3rd in me other hand and use that one to twist ccw. Sometimes they are tough but once broken loose they usually unscrew easily. Slowly pull the nut up and you may find a plug of hair about the size of a mouse.
If you have a rubber seal I just reassemble, if it looks like a paste or silicone it is normally plumbers putty and needs to be cleaned out and fresh putty installed.
Plumbers putty is cheap, roll it like play dough to make a ring around the hole let the ends overlap put the nut back in and tighten. Some of the putty may squeeze out that’s ok just get it tight this is the seal.
Check to see if it flows normally, if it dose quit using drain cleaner it really is a waste on slow moving drains as it just goes down the drain. If needed get a new pop up or just a cheapie rubber tub plug or disk.
I would question any plumber that jumps to $3000 fix before cleaning a drain. And then running a auger or jet down it this may be repairable in 10 minutes. I have done it to my house many times and one of the things I check on houses we flipped in the past.