Keywords issue

hello all, first post but I think it's in the right place!

Firstly, I use a mixture of serpstat for my analysis.
It is great for showing competition etc, but i'm not sure if the keyword monitor works.

My site has 164 keywords, I use Yoast (free) to set my Keywords & meta etc, and the content is as good as my competitors. however, my competitors have around 30 keywords ranking well per site, compared to me having between 3-5 (ranking quite poor)

My web tools is showing around 1000 different queries

My question; Is there a specific way to get more keywords recognised on your posts?
I have reast Yoast Premium allows for 5 keywords per page, instead of the 1 you can currently set.
However, Yoast shouldn't be able to control the amount of keywords I can rank for surely?

thanks

Yoast doesn't control anything.

How old is your site, when was it first indexed etc ?

it's just over a year old, first indexed around 2-3 weeks after going live.

My competitors have over 1000 keywords, compared to my 160

I'm at a loss as to how mine isn't picking as many up, I have read about making sure <h1> contains the keywords you want, but some of the long tail keywords can't be used as a h1 header