I'm going to share my experience with my DD, almost 8, and overcoming her fear.
We did lessons from 6 months old, and she loved them until she was 3 when she got moved up a group too quickly. The fear then set in, and we had lessons where she would only tolerate sitting on the steps and spent most of the time crying and clinging onto me. Then lockdown hit, and when we went back, she was like a different kid....until she moved up again.
We made slow progress, off and on, until she was about 6. Then she went to a friend's pool party. She was in the shallow end, supervised, and having loads of fund. One of her friends pushed her into the deeper end not realising that she couldn't swim independently. She panicked until I got her (literally within seconds). That set her back SO much. So my first advice is to avoid anything like that until she is a confident swimmer.
After that, she was back to being absolutely terrified and crying through lessons. But then she started to get upset on the way to lessons, on the morning of the lessons and even the night before. I felt that forcing her at this point was doing more harm than good, so we decided to stop the lessons altogether and take a long break, with me taking her to the pool for fun only in-between.
This was absolutely the best decision for her, and I don't regret it at all. She definitely needed a break from it. Before we started up formal lessons again, her school class did a term of weekly lessons. This was Sep/Oct last year. I was really nervous about this, and so was she. BUT, she thrived! Doing the classes with her friends was a different kettle of fish altogether. AND she was taller than the pool depth. Both things were a big, big help in getting her to overcome her fear and start progressing again.
We started lessons again, this time with the local leisure centre as this is where she had lessons with the school. We wanted to capitalise on the good experience she had there. She was still nervous for that first lesson, but again she was taller than the pool depth, so she settled in quickly. There were a few wobbles, but the instructor was great. He managed to walk that fine line between comforting, encouraging and making it fun for her.
Each week her confidence has grown, and she soon moved up to stage 2. This meant a move to the bigger pool. She can still touch the bottom comfortably in the shallow end, and then don't go into the deep end at this stage (at least, not at this pool). It also meant a new teacher. We had wobbles again, but again the teacher has been very good and let her go at her own pace. The last 4 weeks or so, something seems to have 'clicked' and she is suddenly LOVING her lessons. She is doing everything confidently and actually looks forward to her lessons! I NEVER thought we would get here, but we did. And I'm confident your daughter can too.
I would recommend checking out the local leisure centres facilities for lessons, are they done in a shallow pool? Can you get her into a lesson group with a friend? Can you speak to the instructors beforehand? Can you arrange to go swimming with some other friends and their kids to get her enjoying the water?
But above all, try not to stress about it. They all get there in their own time. Just continue being that super supportive mum you are, and provide lots of encouragement.