I think you'll find with door locks the issue is not the lock actuator itself, but it's bowden cables, internal to the door.
The bowden cables, which connect the actuator to the moving parts of the locking mechanism, having moisture inside which freezes and causes many symptoms from handles not popping out, locks not releasing, or not latching shut when trying to close the door, regardless of the remote seeming to operate the lock.
Link shows the F Type has 3 such cables:
https://parts.jaguarlandroverclassic.com/parts/index/part/id/152.1079.2460.11508/brand/jaguar/_gl/1%2A1sslzo0%2A_up%2AMQ..%2A_ga%2AMjg3MjE3ODEuMTczNjU5MDAyNA..%2A_ga_6WEX61NFXZ%2AMTczNjU5MDAyNC4xLjAuMTczNjU5MDAyNC4wLjAuMTQ3NDY1MjM5NA../
As the cables are internal to the door application of de-icer or even local heat for a short time usually has no effect, only the inside of the door warming during driving or longer term ambient warming works.
Permanent solution is to either lubricate or replace the offending cable or cables.
For the secondary issue of glass or seals sticking simply apply Gummi Pflege to the seals in autumn. Readily available as a stick to simply run around the door seals and they will simply never stick again for the season.