Child access for a father living in the UK

I live and work in the UK.
My daughter was born 2.5 years ago in Germany (during the pandemic) in the Region of Hessen.
My daughter and my ex-partner lived with me in the UK half of this time, on and off (due to Brexit rules).
My child has spent more than half her life with me, in my home, and with me spending holidays with her in Germany too.

My ex-partner has moved back to Germany (still in north Hessen) with our daughter, and is becoming increasingly difficult, refusing me to take our daughter on holidays to my home or anywhere.
My daughter has grown up a large part of her life in my house, she knows the neighbours, the town, the places to go and have fun, we went to the beach countless times, etc. She is happy and safe here. The mother only opposes to me having our daughter "because she is too young", and refuses to say when I could have her by myself, for even a weekend.

I declared our daughter as my child before birth with the competent authorities, and also after birth.

To make things easier for the mother of my child, she asked me to give her full custody, as I live abroad and cannot sign documents related to school etc. I was reluctant to do this, but she managed to get it out of me. I fear I made a mistake, as I am a caring and loving father.

My ex-partner is also asking for what I perceive a large amount of child support (I have been giving money, more than the British system would say based on my wages).
We have not drafted nor signed any document rleated to this, or anything else regarding support, visits etc

I need legal help to figure out what my rights are, and how to exercise them, as I terribly miss my daughter and feel powerless confronted to the unknown German laws. (I sadly do not speak German).

Many thanks.

Maixent