How to analyze my data of 3 different treatments. (ANCOVA, U-Test) What model to use? (LM,GLM)

I did an experiment with a Mass spectrometer and want to compare the different treatments.

Control: Week 0: Immediate measurement of specimens (n=200) after taking the sample.

Treatment 1: Specimens (appx. n=120) taken from samples stored at -25°C in 100% ethanol. Sample measured after 1, 2, 3, 5, 7 and 12 weeks of storage.

Treatment 2: Specimens (appx. n=120) taken from samples stored at -25°C in 70% ethanol. Sample measured after 1, 2, 3, 5, 7 and 12 weeks of storage.

Treatment 3: Specimens (appx. n=120) taken from samples stored at Room Temperature in 70% ethanol. Sample measured after 1, 2, 3, 5, 7 and 12 weeks of storage.

My questions are: 1) Are the treatments different from the control? 2) Are the treatments different from each other? 3) What are the factors responsible for the difference?

The idea is, that the storage temperature has a strong negative influence on the number of peaks measured. This is also obvious in the following plot:

Dependent variable (response): Peaks

Independent variables:Temperature (categorical); Ethanol concentration (categorical); Time (is it categorical in this case?)

I was told to carry out an ANCOVA but: My residuals were not normally distributed when using a linear model. So I wanted to try GLM in which I had to specify, what distribution my data has. I tested for distributions and found, that a beta distribution was found to fit my data best. The problem is, that it is apparently not possibly to fit a beta regression on the data and use it for an ANCOVA. I found that using quasi-binomial distribution with a logit link could be used as a model in this case. This again lead to not normally distributed residuals. I mean the tests always showed my time as well as temperature had a significant influence on the response, but I cannot use this result since the test is not valid because of the distribution of the residuals.

Am I using the wrong test? Should I just carry out a U Test and compare the treatments to the control? And if so - how can I statistically show that temperature is responsible for the difference?