Give https://recurse.chat/ a try - I'm the developer. One particular advantage over alternative apps is importing ChatGPT history and speed of the app, including full-text search. You can import your thousands of conversations and every chat loads instantly.
Regarding chat history, I've been thinking that people should have ownership over chat history. We are migrating the chats towards SQLite, so your data is going to be a timeless format like files* - SQLite has long term support through year 2050. https://www.sqlite.org/lts.html
We also recently added floating chat feature. Check out the demo: https://x.com/recursechat/status/1846309980091330815