If you're using the internet on the phone, does Android auto-switch between SIMs on dual-SIM phones when one of the SIMs has poor reception?
No. Android doesn't offer such provisions. Pixel 3a line is dual Sim and if Android has this provision, it would have been incorporated in these phones.
It is most likely referring to Dual SIM Dual Active devices where both the Sims simultaneously can be active be it voice or data. As an example you could be talking on SIM1 and yet receive a call on SIM2 which will be put on hold or you could attend that and put the first SIM call on hold (Pixel 3a have this).
(This is in contrast to Dual SIM Dual Standby, wherein if SIM1 is in use, SIM2 becomes inactive and vice - versa. Such phones are cheaper)
Edit: If you are referring to Smart Signal, the FAQ clearly says it doesn't choose the best signal (as your question implies) but merely switches between two networks
Does Smart Signal automatically choose the network with the best signal?
No, with Smart Signal you’ll automatically switch to EE or O2 if you lose signal on Honest Mobile. On some phones you can also manually select which network you want to be on.