What are you hoping to get from a diagnosis? This really depends on how old you are and what phase of your life you are in.
If you’re in school or college still then support should be needs based and you need to ask for it, having a diagnosis versus trying to get one doesn’t always make much of a difference.
For uni some unis require a diagnosis to get support so in that case check if they’ll accept private assessments and if this is the only way to get timely support it seems sensible if you can afford it. However some unis do offer support for those seeking a diagnosis but yet to be diagnosed so check with them if this is your scenario.
If you are in employment a diagnosis would be beneficial and I think they care less about whether its nhs or private so if you need it to get reasonable adjustments from your employer then go for it.
Im currently waiting for an nhs assessment but being given support with a provisional diagnosis, I am currently not in a position to pay to be assessed privately. If you’re over 18 there are services that are cheaper if you do them over zoom and they will still give you a diagnosis without meeting with you in person which could be more convenient
I hope you get what you need and your life becomes easier in the future