Current search engine guidelines

[csdude55]

Can you guys suggest what guidelines one should be considering now for search engine placement?

My main site is just under 17 years old. I target a local region, and have the name of that local region in the domain name. The logo is text, using a styled H1 tag to highlight the name of the region, and I have another area that uses a styled H2 that includes the name of the region. Keyword density for the region name on the homepage is 2.6%. The site shows local news, message boards, classifieds, events, etc, so it's highly relevant for the keyword. It has more than 100,000 unique visitors per week, and is very active. Webmaster Tools shows no search errors on the site.

According to smallseotools.com I have:

Domain Authority: 53
Ahref Rank - 445.76K (no clue what this means)
Backlink - 174.81K
Referring Domains - 421.00
Referring IP's - 240.00

And according to prchecker.info, I have a PageRank of 4/10. It's been a 4 for as long as I can remember, so it hasn't gone down or anything.

A few years ago, my site would come up #1 or #2 on virtually anything you searched for that included the name of that local region. Now, as far as I can tell with Google Webmaster Tools, it doesn't come up at all! More than 95% of my search engine traffic comes from queries that include the website name (which means they were specifically looking for me, they're not a new user that Google sent my way).

But you know what does show up on the first page when I search for the name of the region?

An event page that doesn't have the region name in the website address anywhere, uses the region name 9 times on the page (a density of 1.5%), and that already happened in May. This event was listed on my site, too, but that event listing only showed on Google if you searched for the domain name + the event name.

A senior care facility that doesn't have the region name in the address anywhere, uses the region name 5 times on the page (a density of 1.3%), and hasn't been updated since 2016.

A small museum that does have the region name in the domain, but lists expired events and isn't mobile friendly, nor does it use HTTPS. From smallseotools:

Domain Authority: 36
Ahref Rank - 2.02M
Backlink - 1.03K
Referring Domains - 137.00
Referring IP's - 126.00

And they have a PR of 0/10 (I tested with both HTTP and HTTPS).

Also in the top 10 are generic sites that have little to do with the region: zip-code.com, livability.com, mapquest, worldatlas.com, and familysearch.org.

I'm at a loss. All of the guidelines I've traditionally followed seem not to matter: pagerank, domain authority, backlinks, keywords in the domain and URL, keyword density, the age of the domain, frequent updates with relevant content, and using header tags to emphasize key words. So what does?

[Selen]

The situation is familiar to what I observed on other established sites. Users trying to find the site using your brand name means there's nothing wrong with your site.

[iamlost]

Unfortunately all those numbers mean little except that you are using SEO tools. Which links Google sees and how it weights/values each is only known to Google. While Google is a popularity engine it also tends to look for commonalities of 'celebrity' gaming (among other things), which can both identify bad practices as well as false positives. Given the number of sites available in a given niche, far more than shown in query results, Google is quite happy with false positives below some threshold; naturally, wrongly so identified publishers are not; however it is Google's game.

That said, while 174,810 backlinks are nice,
---174,810 backlinks / 421 referring domains = 415 backlinks per referring domain might be viewed as a considerable concern. Or not as averages are not reality.
---421 referring domains / 240 referring IPs = 1.75 domains per referring IP might be viewed as a concern. Or not as averages are not reality.

I contrast your shown comparison site:
---1030 backlinks is relatively low but not unusual for local niche sites.
---1030 backlinks / 137 referring domains = 7.5 backlinks per referring domain is much less a concern.
---137 referring domains / 126 referring IPs = 1.08 domains per referring IP looks much nicer.

More than 95% of my search engine traffic comes from queries that include the website name (which means they were specifically looking for me, they're not a new user that Google sent my way).

This means that Google is mostly/only sending navigational traffic aka traffic that pretty much requires Google show and emphasise your site in query results. It is NOT sending a significant amount of competitive organic traffic and that is definitely a critical problem. In essence, while the level of Google traffic may be substantial it is specific to your site and NOT to your niche nor to your keyword when not explicitly coupled with your site in query.
Note: well done on the level of nav traffic, most sites get negligible in that regard.