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Just wanted to give a little update.
First, thank you all for your explanations and suggestions.
My score somehow did not bounce back up after the freedom unlimited reported a balance of about 300$ again. The score went up by like 10 points or so compared to a 0$ balance that it had the month before. To me it seems that the drop in score might have been mostly caused by closing my secured Wells Fargo card. I knew that it was not ideal to close this card but I did not want to pay the 25$ fee for a secured card that had no chance of ever being unsecured.
In the end I decided not to apply for the Citi Double Cash right now. I have two cards now and a total credit limit of 16300$. I am happy with that. Honestly, I did not expect to get such high limits from Chase given that my credit history was only based on a secured card with a 300$ limit when I first applied. For now I will just wait a few months until my scores are back up again and then apply for the Double Cash.