I came in through Alicante airport on 28/12/20.
I had to produce my passport and TIE at passport control.
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My QR was scanned and authenticated online at a "temporary" checkpoint just after passport control.
My PCR was scrutinised at the same checkpoint, although as there are many providers of PCR tests, an online authentication wasn't possible (at that time).
If you have been through Alicante departures lately, you will have seen that all UK flights are dispatched from a segregated area, with an extra layer of passport e-security. The extra security (an extra set of e-gates) was installed in 2019. ROI flights are also dispatched from this area (due to the UK/ROI common travel area).
If the "wet stamp" is used on entry, it will probably be for the benefit of police officers who do not have access to the e-passport security facilities out on the street.
When visiting the USA, Brits currently obtain an online visa via the ESTA system. The visa can be printed out and carried at all times ... for scrutiny at border controls (although border officers have it onscreen), by police officers, etc. The ESTA has an end-date, beyond which the carrier is illegal. The EU plans to have a similar system in 2022, called ETIAS. So the ETIAS visa can be carried as personal ID.