"internet platforms that organise and promote large amounts of copyright-protected works uploaded by their users in order to make a profit"
Would include https://news.ycombinator.com as well. It does organize and promote user comments, quotes, references which are of course copyright-protected works as anything created in the EU member states is, including user comments. Now "Hacker News" does not make a direct profit of the content. It is a side-line to a profitable business. It is however trivial to argue that the fact it is a side-line by a for-profit company it must in some way contribute to that. This has been done before.
The term upload does not exclude anything, because there is no legal or technical distinguishable difference between upload and post. The law could have read 'provided by their users' and the legal implications would be the same.
All sites that are for profit and allow anything from their users are affected by this. This would also include online games that allow users to chat.
I don't agree that its intentions are that clear. Nobody likes a leech, but that does not mean that we should kill all animals to prevent leeches.
"And if it changes the internet as we know it today, is it that bad? It will push people to self publish instead of relying on "platforms", like the old internet."
This seems to be a call to the internet being just for the technologically savvy. No great number of people are going to self host and any form of support for people self-hosting from a for profit company will run into article 13. Moreover what I remember from the old internet is not self publishing, but the social gathering on IRC, newsgroups, etc. Something that will be impossible to do at our current scale without for profit companies or government backed services. The first will run into article 13, the second one is a non-starter.