Should I follow COVID restrictions for the destination country only or also the layover country?

TLDR: Assuming you don't exit the transit area in a country, you only need to follow their transit rules. But in your case you'll have to exit the transit area and consequently you'll have to follow the requirements for entry.

Details:

See https://reopen.europa.eu/en/map/DEU/7004 for the German transit rules (there are none if you don't exit the transit area, but in your case you'll have to exit the transit area):

Transit by air

Changing flights without leaving the international transit area of an airport does not constitute an entry into Germany for the purposes of the relevant regulation. In these cases the digital entry registration, requirements for mandatory testing or providing proof of vaccination, quarantine regulations and travel bans from countries affected by coronavirus variants do not apply. This only affects travels from a destination outside the Schengen area and with a destination outside Schengen area – for example from Moscow (outside Schengen) via Frankfurt (transit) to Buenos Aires (outside Schengen).

When travelling from or to the Schengen area you will need to leave the international transit area of an airport – for example when travelling from Moscow (outside Schengen) via Frankfurt (transit) to Madrid (Schengen area) or the other way. Therefore, these travels do constitute an entry to Germany and the selected requirements for entry, regarding testing proof, proof of recovery, or proof of full vaccination, must be followed.

https://www.iatatravelcentre.com/world.php also mentions transit rules if any.

If you plan on touching down in a country as part of an international trip, you will always need to follow the rules of all countries involved. Specifically in your case:

• you need to follow the rules of your country of origin (here: the US) for leaving and re-entering including potential quarantine
• you need to follow the rules of your layover(s) (here: Germany) concerning permission to transit, details of said permission, potential requirement to isolate, exceptions from the requirements to isolate, etc.
• you need to follow the rules of your destination (here: Spain) concerning permission to enter the country, potential requirement to isolate, etc.

The Covid-19 pandemic situation is really no difference from Your Standard Pre-2020 International Airline Trip™, except that they are more volatile since the pandemic began and they now also happen to apply to travellers with passports of western developed nations.

In your case, the situation is slightly more complicated as your layover will require you to go through immigration (and there will be no further immigration between your layover and your destination) – a feature of the Schengen area. As German immigration has no way to surveil you to confirm that you are indeed taking a flight out of the country very soon, you will have to comply with all German regulations for entering except where exceptions for intra-Schengen transits have been explicitly made.

Note that exceptions referring to international transit (i.e. not leaving the airport transit zone) do not apply to travellers entering the Schengen area on a layover.