I'm aware that HTTP/2 is using only https.
My existing implementation are all HTTP/1.1 with http protocol for all the urls on the website.
To add HTTP/2 support, without change the html source code, I plan to redirect all http requests to https on the nginx server block level.
With this approach, is there any drawback/impact on search engine indexing and bot crawling?
Many, many references for how to migrate from HTTP to HTTPS online so just Google this. Or ask/search at sister site of webmaster.stackexchange.com. Once on HTTPS there's no real difference in SEO terms to migrate from HTTP/1.1 to HTTP/2.
Basically it's that (set up redirect) but need to ensure HTTPS is set up correctly, that all resources on your page (e.g. external and internal URLs to load images, JS, CSS... etc.) are HTTPS, update sitemap, register HTTPS URL at Google Search Consle to keep an eye on errors. And then wait. You'll probably see an initial dip in search traffic but if you've done it right that should quickly recover.