OK, I've found the following in the Article 3 of a MiCA draft:

(8) ‘crypto-asset service provider’ means any person whose occupation or business
is the provision of one or more crypto-asset services to third parties on a
professional basis;
(9) ‘crypto-asset service’ means any of the services and activities listed below
relating to any crypto-asset:
(a) the custody and administration of crypto-assets on behalf of third parties;
(b) the operation of a trading platform for crypto-assets;
(c) the exchange of crypto-assets for fiat currency that is legal tender;
(d) the exchange of crypto-assets for other crypto-assets;
(e) the execution of orders for crypto-assets on behalf of third parties;
(f) placing of crypto-assets;
(g) the reception and transmission of orders for crypto-assets on behalf of
third parties
(h) providing advice on crypto-assets;

and they further define what all of that means.

Based on this, I believe that neither miners nor LN nodes are CASPs. However, LN nodes that offer swaps between Taro tokens and plain sats are definitely CASPs.