Both are directives to google. All of the "rel=" links are directives, including hreflang, alternate/mobile, AMP, prev/next
It's not really necessary to use a canonical tag in addition to any of the other "rel=" family links
A canonical tag says to Google: "I am not the real version of this page, I am non-canonical. For the canonical version of the page, please follow this canonical tag. Don't index me at all, index the canonical destination URL"
The pagination based prev/next links say to Google: "I am the main version of this page, or one of the other paginated URLs. Did you know, if you follow this link - you can find and index more pages of content if you want to"
So the problem you create by using both, is creating the following dialogue to Google:
1.) "Hey Google. Follow this link to index paginated URLs if they happen to have useful content on"
*Google goes to paginated URL
2.) "WHAT ARE YOU DOING HERE Google!? I am not canonical, go back where you came from #buildawall"
*Google goes backwards to non-paginated URL
3.) "Hey Google. Follow this link to index paginated URLs if they happen to have useful content on"
*Google goes to paginated URL
4.) "WHAT ARE YOU DOING HERE Google!? I am not canonical, go back where you came from"
*Google goes backwards to non-paginated URL
... etc.
As you can see, it's confusing to tell Google to crawl and index URLs with one tag, then tell them not to with another. All your indexation factors (canonical tags, other rel links, robots tags, HTTP header X-Robots, sitemap, robots.txt files) should tell the SAME, logical story (not different stories, which contradict each other directly)
If you point to a web page via any indexation method (rel links, sitemap links) then don't turn around and say, actually no I've changed my mind I don't want this page indexed (by 'canonicalling' that URL elsewhere). If you didn't want a page to be indexed, then don't even point to it via other indexation methods
A) If you do want those URLs to be indexed by Google:
1) Keep in mind that by using rel prev/next, Google will know they are pagination URLs and won't weight them very strongly. If however, Google decides that some paginated content is very useful - it may decide to rank such URLs
2) If you want this, remove the canonical tags and leave rel=prev/next deployment as-is
B) If you don't want those URLs to be indexed by Google:
1) This is only a directive, Google can disregard it but it will be much more effective as you won't be contradicting yourself
2) Remove the rel= prev / next stuff completely from paginated URLs. Leave the canonical tag in place and also add a Meta no-index tag to paginated URLs
Keep in mind that, just because you block Google from indexing the paginated URLs, it doesn't necessarily mean that the non-paginated URLs will rank in the same place (with the same power) as the paginated URLs (which will be, mostly lost from the rankings). You may get lucky in that area, you may not (depending upon the content similarity of both URLs, depending whether or not Google's perceived reason to rank that URL - hinged strongly on a piece of content that exists only in the paginated URL variant)
My advice? Don't be a control freak and use option (B). Instead use option (A). Free traffic is free traffic, don't turn your nose up at it
or by simply denying Gooblebot's user-agent, access to certain pages entirely