UCSF generally has good default advice for this stuff:

When measuring hormone levels in patients using injected forms of estradiol, a mid-cycle level is often sufficient...
- https://transcare.ucsf.edu/guidelines/feminizing-hormone-therapy (search for "Monitoring hormone levels in patients using injected estrogen")

At the risk of overcomplicating it, there are reasonable arguments to be made for testing at different times depending on the goals of your testing. However, the half life of EEn is so long that once you're on a stable weekly injection cycle your serum estradiol levels should be steady enough that it doesn't practically matter when you test. You can play with a pharmacokinetic simulator here to see what I mean: https://transfemscience.org/misc/injectable-e2-simulator-advanced/