You must understand how they are index to understand the impact
Webmaster tools like you say (dude! we are in 2022 now, GSC ffs), try to index you straight away, both from manual submission, or sitemap or even, API. It's like the artificial way to say to Google, "hey I'm here". It's not better or worse, it's simply the way to keep Google updated.
On the other side, this linkdexing tools use many techniques , but all go through the same idea: they use pages where they publish the links sent to them. Those pages could be owned by them or not. Generally best indexing services have owned pages because they can "execute" the trick: they send via API those pages where they have put your link to GSC. The idea is that the crawler, get there, crawl your link and go into your page and crawl and index it. You coul think that is more natural that sending to GSC straightly, but there is a huge problem: you are sharing page with hundreds of other links which look SPAM AF.
This is why, from my point of view, linkdexing is a very bad idea for your own sites. If you don't own a site (lets say blasted links, or a parasite), it makes A LOT OF SENSE to use linkdexing tools. But if you own them, just shoot to GSC
There is a third trick that some people use: your own linkdexing site. If you own a MEGA site (say DR60+), that you know is being crawled on a daily basis naturally, just place some links to your sites there with certain degree of crawlability (for example in the footer of an article). This will BY FAR the best indexing technique of all, because it looks omega natural.
But personally, I think that linkdexing for your own site on any of it's forms it's overcomplicating your existence unnecessarily. Just forget about manually/programmatically indexing or do it through GSC/API. Don't waste your time on weird methods.
