Can you post a picture? That would help us offer suggestions.

For right now, search for a mow-and-blow person. (They’re all over my FB feed right now.) Schedule them regularly so they can keep the stuff under control while you save and think about what you’re going to use the yard for. No need for a plan until you decide your priorities.

Are there any plants or trees that are salvagable? Prune them to shape and get a hoe and wack the weeks down from around them.

Spread Preen according to instructions and you won't get any more weeds popping up because it stops seeds from sprouting.

Do you have a lawn? Outline a space in bender-board, prepare the soil and order sod to be rolled out. Use Weed and Feed on the lawn unless you are against herbicides.

Once the lawn and weeds are under control, plant flowers around the perimeter of the lawn. Get a hose and sprinkler if you don't have a watering system but I recommend an underground lawn system plus a drip system for the plantings.

A lawn surrounded by flowers and shrubs is still the most reasonable option, quickest and best use for a yard without construction of gazebo, deck etc. Those can be added later.

Here is a casual style and a formal style lawn with plantings:

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What do you mean by "backyard overgrowth?" Weeds of any sort in the lawn can be mowed. It will look like a lawn. Sure, if you inspect it, you won't find every bit is an identical blade of an identical grass, but it will look good.

If you are talking about weeds in your garden beds, then mulching and more dense plantings is probably the answer.

If you are talking about shrubs that you want to stay in nice, round, highly-unnatural pruned shapes, well, then, change your expectations, prune more often or hire someone who will prune for you.

If you have a bunch of unruly shrubs in shady places that send long branches out in search of more light, then replace with something more suited for the location.

You mentioned access. Stepping stones are good to make a path for avoiding dirt and grass. We used fake flagstone ones from Home Depot across the lawn.

HD also had recycled rubber pavers we used for a patio and front entry walk. Very light weight and easy to lay down. They hook together with plastic pieces if you need to.

These are cheap solutions we used that are so nice we kept them and have lasted for years.

Added a couple pictures.

Yep - that's overgrown. Purchase a lawn mower and start mowing those weeds down, then see what it looks like.

Is that pretty much it in your 2 photos, or is there a lot more?

I agree it is overgrown, but I am not sure with what. On zooming the pictures, some of the plants look like they could be plants that escaped from the flower beds.

I would cut every thing that is not a flower bed and see what you have. I would try to identify each of the plant, not necessarily complete but close enough to tell if it is a weed or desired plant. Mow the area for a couple of months and then in the fall if the are you have seen not improved, treat the area with a broad leaf weed killer and spread some grass seed, followed by fertilizer.

We planted some woods poppies several years ago, they spread and we love the pretty yellow flowers that bloom heavily in the spring but continue to bloom all summer. They must be keep in their bed room so must be cut when every they leaves.

So depending on what was planted in your flower bed you may enjoy them but have to fight them continually.

Alternately, once the weeds are chopped down, you could define a mud-free seating area by laying out and leveling a space and covering it with a nice thick layer of shredded bark mulch. Until your soil is prepared for planting, create garden accents with large pots filled with flowering plants.

Put on your boots to explore out there!

If you can, may have to be after string trimming to see what’s what, identify one of more “ pathways “ through the area, that seem useful, I.e. not through an existing flower bed or hedge, and try to keep that closely cut. Even can put a few pavers there, though I would not spend much to get them or even get them at all unless it’s really muddy out there.

Because , this would not be for a permanent path, but just to help you feel comfortable getting out there, checking, weed- eating or using a bit of Roundup.

Thanks to @Christopher CNC for idea for rough paths to encourage getting out there.