The Lenovo ones don't support eGPU well because they (like the other big names) have custom graphics silicone that needs custom drivers, and they haven't bothered to add support for eGPUs to their drivers, although the hardware supports it.
The ayaneo and onexplayer just use the standard OTS amd graphics hardware and standard amd drivers, which do support it.
Idk if the bazzite has found custom foss drivers that add eGPU support to Lenovo devices, and also I'm basing this on reviews a few months old from people who are using the out-of-the-box software, not installing a new OS on it. IIRC someone used the Lenovo with SteamOS and it didn't support eGPUs but it's been a while so I may be misremembering that review, or it may have been a preview or speculation or something.