The last airline is responsible to you, even if the other was the one that misplaced the bag.
(My 2c is to get what you genuinely need - if you wait to be "approved", it raises questions about how badly you needed the things. Hopefully you have access to a credit card to cover the interim expense even if it is reimbursed as it should be.)
Your EU passenger rights are here
https://europa.eu/youreurope/citizen...en.htm#luggage