I'm not sure what the testing guideline is for Senvelgo. There may be info here as well as info your vet may not have informed you of: Info - New Treatments for Feline Diabetes
I think it would be ideal to test before giving each dose of Senvelgo just so you know what your cat's level is. Senvelgo is only dosed once a day. Many people find it easiest to test while the cat is busy eating.
Getting a test 12 hours later would be a good idea. A few random in between tests is ideal so you have a picture of how your cat is responding. FDMB members track blood glucose levels on this spreadsheet: https://felinediabetes.com/FDMB/threads/how-to-create-a-spreadsheet.241706/ It's easily shared with other members and the vet.
How many hours after the dose of Senvelgo did you get 377? One number doesn't tell much other than your cat has a high blood glucose level. Normal cat levels are roughly 60 to 150 mg/dl.
Is there a reason why your vet prescribed Senvelgo instead of insulin?
What are you feeding your cat? Diet is an important part of managing the diabetes, just like it is for Human diabetics.