I’m in Neuroscience. My favorite way to keep up is rss feeds of the 5 best journals (100-200 titles per week), rss feeds to the relevant pubmed search terms (20-50 titles per week) an google scholar email alerts to some of the most relevant researchers in my field, auto forwarding to kill the newsletter, and read through rss (50-100 titles per week, lots of duplicates). So every day I aim to open the rss reader and burn down the unread count. Papers that are really relevant to my research tend to show up 4-5 times over 2 weeks this way, so it’s hard to miss it. Which journals: you know that if you have been in the field for a while, if not, ask your colleagues and mentors where they publish and what they read.
Bad papers sliding through the cracks: it happens, you don’t know unless you read it.

Physorg is a great resource for someone who is not currently fully educated in the field but has a strong interest. They do really good summaries of each topic and provide just enough context to go and find out more. They also do have good RSS feeds available, so you can easily use whatever client you like to get their content.

As for FOSS clients, just have a look in F-Droid and you will find a bunch. I use Feedflow at the moment but I have tried a few from F-Droid and they are all similar. On desktop I would recommend looking at a different one depending on your desktop environment. On EndeavourOS with KDE I have used a few but be one included with the Kontact suite is fairly good.

Read as much as you can, investigate the authors, go to conferences, meet them, ask questions, investigate their funding, try to replicate their results.