Solved

League Change No Design Points

If you join a league at the beginning of a season you should get the amount of points as if your current active Chief Designer worked a full season on the car. Now to figure out if it's just the wrong message displayed or also the wrong car: Your current CD joined your team just 2 races ago and is 1 level lower than your team. So the question is how good was your former CD and how many design points you got after joining for each of the average (not strength or weakness) design areas? Also, as with every team else at the start of a season, you don't get points to spend.

Yes, that message isn't for joining at the beginning of the season and therefore misleading.

Higher level doesn't necessarily result in a better starting car, that's independent of level, but as leveling settles down quite a bit once the level moves into the double digits it's easier to consistently have the best possible Chief Designer all the time, although at the really high levels it gets difficult again to find one with good strength/weakness combinations as they are very sought after.

As a starting point: To get a good starting car into a season you need a 5 star, or 4.5 star that's the same level as your manager level, CD active for every race during the previous season. For more info see this guide https://igpmanager.com/forum-thread/8281 is a good starting point. Some track and tyre related info is outdated as the tracks are in a currently still ongoing process of updating, fixing and tweaking, and the tyres changed a while back (also considered not final) but the general thoughts about how the game works are still valid.