First time lawn owner advice

I bought my house in June and this spring is the first time I'm putting some effort on my backyard lawn.

I've watched a few videos on lawncare and I've been trying a few things.

I've mowed the lawn on my mower lowest setting, I removed the large weeds and I manually scarified/dethached it. I tried aerating it with a manual aerator, but only managed to do half of the lawn as the pipes were getting clogged after only a couple of inserts and it was a massive pain to unclog it… I must be doing something wrong as there is no way this is acceptable as a product (just venting).
I also applied a product to suppress weeds, and supplement the lawn with iron and nutrients.

My lawn is now in the condition of the picture. Not looking great…

I believe the next step is overseeing, but I just want to check with you experts if there is anything I should be doing before applying the seed, or any advice for this first time noob here.

Thanks