I'm in a dilemma of wanting to change my career from a Data Engineering background to a SWE one.
My dilemma is about me not having too much of a coding background (too much SQL) and not wanting to do badly, alongside with probably having to accept less pay.
What company are you working in now? How senior are you?
If your company has a program to allow internal transfers, I highly recommend pursuing that instead of applying to new companies. You'll have a clear advantage in your current company, assuming your performance has been good.
If you're very senior, you should be prepared for a level downgrade since your companies may not give you "credit" for the years of experience you have in DE.
Most of the tactics around applying for jobs will apply here. Leverage your network for referrals and build stuff as proof of work.