Would I need to go thru Immigration in Zurich to connect to Kyiv? SwissAir entire trip

The word “immigration” seems to be creating a lot of confusion so here is a detailed description of what should happen during your trip:

1. When leaving Spain, there shouldn't be any police check, the airline may or may not check your ID for different purposes.
2. When you land in Zurich, there shouldn't be any systematic check (although some spot checks are always possible, including enforcement of Covid-related entry rules when relevant). You would therefore enter Switzerland and be able to exit the airport without going through any formal immigration check.
3. When leaving Zurich, you have to go through a Schengen exit check performed by the Swiss customs (Administration fédérale des douanes / Eidgenössische Zollverwaltung) or possibly the local police. That's the only “immigration” check in this part of the trip that is mandatory and systematic.

Both Spain and Switzerland are part of the Schengen area. So you will not have to go through passport control (immigration) in Spain, but will do so in Zürich, where you will be leaving the Schengen area.