Right now when you have a certain replay or map search query running in the client, it resets when you tab out. So for instance I have this replay search opened: 1500+ ladder 1v1 games from 2022 or whatever. If I then go to aeolus and back, it resets the query so I have to navigate back to where I was from scratch. Same for the map vault.
Having the client remember what search you had opened, would be a nice QOL change. Especially for people that search a lot of replays and maps for instance with making the matchmaker pools/tourney pools.