– Playing in the official Champions League qualifying rounds is enough, no need to enter the group stage.
– If the Saudi top league changes name it will still count.
– If a Saudi team joins a European league it will still count.
– If Champions League changes name or format it will still count, as long as the Saudi team is playing in a European tournament at, or above, the current Champions League qualifying stage. E.g. if a top tournament is split out above the Champions League with 8-16 teams, then a tournament below it would count as long as it's not more similar to Europa League. Let's say at least 16 out of the top 32 teams (as implicitly ranked by UEFA by structure of tournaments) need to be in the tournament for it to count.

https://www.goal.com/en/news/saudi-arabia-champions-league-wild-card-uefa/blt3f9f2cbba89a50e5

Saudi Arabia want a team in the Champions League as as they plan sensational 'wild card' request to UEFA | Goal.com

Saudi Arabia reportedly want a team in the Champions League as they plan a sensational 'wild card' request to UEFA.