Stopping smoking makes me wide awake all night and wanting to nap all day. But vaping has prevented most of the withdrawal symptoms for me and after three weeks I feel normal.
Since you gave up so long ago I'd be willing to guess that your sleep problems are unrelated, since your body has had plenty of time to adjust.
I am so prone to insomnia I once had crippling addiction to diazipam, now I live by these rules:
No caffeine after 5pm
No food or drink two hours before bed
No physical activity two hours before bed... (There are exceptions)
No phone, ipad, laptop in bed.
No T.V in the bedroom
Bedroom is for sleeping only, must be a clean and relaxing space
Bedroom must be as dark as possible
Read a book
Don't try to force sleep, after half an hour get up and do something else, then try again
Reduce your nicotine intake
if you do all that you'll sleep like a Hindu cow.