Unfortunately there's no great or even really good solution to getting the Live TV content (via the antenna hooked to the TiVo you already have) and the streaming content. Your Roamio should support a mini, but... you'll need to get network cabling to the location where you want to use the mini and you'd have to make sure the Roamio is on the same network. Assuming you can easily run network cabling to satisfy that requirement, no big deal.
The TiVo Stream 4k is a decent device, not terribly expensive, but it has absolutely nothing to do with the traditional TiVo -- there's no TiVo client on it, no ability to access the Roamio to show content from it, etc. Instead, it simply allows you to stream content by running Android TV apps. It has a strong variety of streaming app support which is great, but again no way to get any of the content you recorded on the OTA Roamio, so you'd have to find that content on say Hulu, or some other service or only watch that content from the TV with the Roamio connected to it, or, as you were realizing you could switch inputs back and forth to get to the Stream when desired versus the mini when that was preferred.
Switching inputs sucks, but.... well, that's just kinda how it goes.
If your Roamio OTA has lifetime, you might be able to sell it off to someone else and instead replace that with an HDHomerun device. The latest of those supports 4K broadcast (where broadcasters are broadcasting with that standard) but the amount of content there is a bit weak so far. It supports standard HD TV signal as well though, and you could potentially add the HDHomerun's storage partner device to get one year free of their DVR service. Personally, I think the HDHomerun DVR service is weakened by their guide and the user interface. The Channels DVR is much nicer (my opinion) and will use the HDHomerun tuner, but Channels doesn't use the HDHomerun's own storage device and instead needs another device working as the storage server. Much more complicated, but not a bad solution if you wanted to work from the same input and device all the time as you could then just use the TiVo Stream 4K as your gateway to everything else.
If the HDHomerun's own DVR and guide don't annoy you, the per year fee for additional years of DVR service isn't too expensive, and the app is free so easily installed to use on the Stream 4K's or similar devices.
Best of luck to you regardless of how you proceed.