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Discord is on a quest to become a better messaging app
(www.theverge.com)
This is a most excellent place for technology news and articles.
On reddit you can simply use a tampermonkey script to remove your data. On discord, there is no option to delete all your messages. To the extent that there's a discussion worth having about whether Discord is following the GDPR.
Not tackling security issues means discord is okay with third parties exploiting the software to gain info about certain users - which could include hacker groups or government actors targeting single targets.
I dont think discord can give individual messages over, legally, although they are stored unencrypted on Discord's server.