Seeing a lot of people saying headphones are not BIFL but there's plenty of headphones out there that have lasted a very long time. r/headphones r/AVexchange are decent places to look. You just need to spend more than the bare minimum. If you are in a larger city area you can also find meetups where people show off their gear for others to try.

As for wireless and bifl. If you are handy with a soldering iron you can likely replace the battery after 5 or 10 years when it finally becomes unusable but eventually you will struggle to source replacement batteries. Sadly many can't power the drivers without a working battery.

Going with a budget of $400 here are some options:

• Dongle and a pair of good IEM (in ear monitors) ~$100. General consensus is Moondrop Aria or Etymotic ER2SE. I love my er2s as they double as really good earplugs for working with power tools. The fit took a while to get used to. My wife loves her Arias after killing several $20 pairs of KB Eears. IEMs were originally meant for musicians on stage so do a very good job of passive (think earplugs) sound isolation.
• There are products that will give you bluetooth to headphone jack or double as a better dongle. Personally I have a Fiio BTR 5 which can be a usb c dongle when the battery dies. I run the er2 cable inside my shirt and into a pocket and is almost as convenient as the airpods pros I ended up selling after the ANC chip died repeatedly. These can also drive higher impedence (ohm) headphones that start showing up as you go upmarket. $120
• I worked at a radio station in college and bought a pair of Sennheiser HD280s in 2006ish for use in the studio. 3 years ago I finally got annoyed at the fake leather flakes getting everywhere and replaced them with some nice lambskin stuff. I fully expect this pair to last another 10 years at least. They are okayish as closed back headphones at passive sound cancelling. Not nearly as good as the Etymotics but have worked really well for general open office environments and all day comfort. 280s are not widely regarded as crazy good sound quality but low impedence Beyerdynamics are similar price and have a cult following. New these are $100ish.
• I also have open backed headphones that are really nice if you have a quiet place to listen to music. Bass is a little weaker but the soundstage is bigger and they let air vent so are more comfortable for longer. They are terrible at sound isolation. Sennheiser HD600s are 200ish used and are widely regarded as a benchmark headphones need to beat. The stock pads aren't great and you'll need something more powerful to drive them but with aftermarket leather pads they definately will last you a long time. $200 + $120 for a BTR or similar.
• Koss on ear headphones also have a cult following and are very cheap.

tl;dr: Low impedence dynamic driver headphones that have a 3.5 (1/8in) headphone connector can last a very long time.

Dankpods on youtube got me into this rabbithole a couple of years ago. Generally hilarious Australian drummer. https://youtu.be/MAevLnhaU68 Runs a very active discord server that would also be able to give more options than I've explained.

Headphones show also has a similar round up. https://youtu.be/w5EhQlmD-0Q