Looking for a Beeper alternative that keeps all my chats in one inbox. What are people using?

Depends what bugged you about Beeper. If it was the reliability, or the fact that everything bridges through their servers, then a local-first desktop app is the direction to look. Spanbox is the one I settled on. It loads each service as its own real session on your machine, so WhatsApp is actual WhatsApp Web under the hood, not a bridge, and nothing is relayed through a middle server. One unread list across all of them, and it is free. That said, be honest about what you need. If you specifically wanted iMessage on non-Apple hardware, that is the one thing the bridge apps do that the session based ones cannot. For everything else (WhatsApp, Telegram, Slack, Signal, the usual) the local approach has been far steadier for me.

Been running Spanbox for a few months after Beeper kept dropping my Telegram. No complaints, it just stays open in the corner and I stopped opening six tabs.

Franz and Rambox are the old guard if you want to try a couple before committing. They do the tabbed thing fine. I moved off them because they got heavy with a lot of services loaded, but your mileage may vary.