How to replace an old concrete block wall inexpensive yet sturdy?

See if this helps: https://www.todayshomeowner.com/how-to-build-a-stackable-block-retaining-wall/

Good luck!

the best way to do this is remove them put down a new base of pea gravel then reset them

I agree with the previous comment. The blocks look fine, but they need to be reset. Put down a layer of pea gravel as a base, then a thin layer of sane to set the blocks in. Then, restack the blocks and they should last for years and years

What a beautiful area. If the fence is yours I'd power wash it first then weed and thin out the plantings or vice versa. Expand the planting area by making the border larger more circular or wavy, paint the old bricks with exterior paint in your favorite color, replace the brick or eliminate them altogether, add black mulch. You can include a bird bath and a fountain if you like. Include a few solar lights, and voila! a new one of a kind garden. You can always hang an old mirror on the fence and attach a few old windows painted in your favorite colors as a focal point. How about an old wooden chair with a potted plant? Have fun and enjoy your new creation.

I have recently discovered gabion walls, which are like wire cages you fill with rocks, bricks, whatever you want. There's lots of videos and posts on them. You could use your old blocks for center fill and pour more decorative rocks around them. I have a block wall that is leaning, and am researching the possibility of encasing it with a gabion and filling with river rock or stacked stones on the exposed sides. Rebar for reinforcement and anchoring. I'd rather make wire cages than mix concrete! :)

Rebuild, but this time pore a concrete footing an put in rebar to do it right.