Here's the other way I solved the problem, though it's a workaround.

You can only pair a single Tivo remote, but you can pair several non-Tivo BLE remotes with the Tivo Stream 4k. If you try to pair a Tivo remote as an arbitrary non-Tivo remote, it outsmarts you and recognizes it as a Tivo remote anyhow. BLE universal remotes are available, though not exactly plentiful. But it turns out that you can use an Amazon Fire TV remote with a Tivo Stream 4k, and that's what I am currently using as the second remote. There are several models and generations of Fire TV remotes. I got the kind that is "with TV controls" (volume up/down, mute, and power) but without the dedicated streaming channel buttons.

This doesn't have all of the same buttons corresponding to the Tivo remote, but it does have the ones we use most of the time. Notably, it doesn't have a numeric keypad, but it turns out we don't use that at all. The voice button does prompt the Tivo Stream 4k to listen, but it doesn't pick up any words. Perhaps that's due to some difference in protocol, but we don't use voice searching either. (Call me old fashioned, but all this voice command stuff is a bit too Jetsons-y for me. What next? People using voice to communicate with phones?)

There is some kind of price premium on BT remote controls. I don't know if there is some 3rd party cost involved or if it's just "what the market will bear". When I got my second Tivo remote, it was just as cheap to buy an entire Tivo Stream 4k locally as it was to buy an extra remote (from the Tivo web site) and pay for shipping. So, that's what I did. I've never even powered up the second Tivo Stream 4k dongle. The situation is quite similar for Fire TV remotes. The cost of a remote is not a lot different from buying an entire Fire TV stick. (That's true at least for the BT models. There are some TV sets with  Fire TV software built in. Those use IR remotes, and those are pretty cheap. They are also not useful for this purpose.) I was lucky to find someone selling a used Fire TV remote on an auction site.

These device makers have all kinds of tricks up their sleeves, and I'm not privy to most of them. The TV controls on the Tivo remote for the Tivo Stream 4k work with my TV. (I don't remember if I had to do something to make that work. Probably.) The Fire TV remote that I had for my Fire TV dongle also controls the TV correctly. The replacement Fire TV remote did not control the TV at first. So, I paired it with my Fire TV dongle as an additional remote (hey, an additional device-specific remote ... have as many as you want, what a concept!) and went through a painless procedure to teach it about my TV. Then I unpaired it from Fire TV and paired it with my Tivo Stream 4k. Hey, presto: TV controls. I could not find a way to teach it about my TV via the Tivo Stream 4k user interface.

Using that Fire TV remote with my Tivo Stream 4k works well enough for me, and it takes away the time pressure for implementing blexMang. I let my couch partner use the original Tivo remote so I don't have to send them to re-education camp.