I would ditch the Yagi and make a biquad antenna instead.
In the distant past (back when I speht a lot of time in nearby cafes and needed to use my home Internet connection, as I did not want to pay for theirs) I made several biquad antennas based on designs I found on the web.
I still have one of them and I went back recently to see how well it resonated since now I have a vector network analyzer.. It was spot on.
A biquad is very simple, as long as you get the measurements and use the right kind of wire. (i use approximately 1 mm copper wire thats used in most of the house wiring here now.
Basically the driven element is a piece of wire bent into two squares and fed in the middle.
In fact, you might be able to use a biquad element as your driven element for this antenna. However, here is the thing, if the two sides are going out on the sides, you feed the biquad in the middle and its a vertically polarized - not a horizontally polarized antenna.
Its entirely possible that the addition of directors to your biquad in the appropriate polarization will give you an antenna with a lot more gain, if that's what you want, it also solves your matching problem as nothing could be easier than bending the wire to the right shape. I would consider that.
Its very forgiving and has a substantial enough amount of gain to support a fairly decent range without needing any fancy equipment to build. Even without directors, just a reflector at the right distance, which is 1/4 wavelength of 2.4 GHz. That you may need to tweak a bit.
You could also use a corner reflector which has the advantage of having the distance be non-critical, Just make sure you remember that a biquad's polarization is the direction represented by the two feed points, so even though some might think it was horizontal, its actually vertical.
Again, what you'll end up with should fit well into your mental box of what TV antennas look like, because all these designs are a well explored space used frequently for commercial TV antennas..
If you plan to build antennas, and have a spare $75 or so, you should consider going to Tindie.com and buying a nanovna 2 from its designers. That money is money well spent as its not just a fantastioc deal its literally a spectacular one, and you will have a very powerful tool for evaluating things like that antenna you made and nothing will tech you faster what happens, at least in the impedance matching and resonance domain. (However it cannot test the gain and pattern for you, that is just as important) .
But you'll have the best tool you could possibly find without spending literally what a car cost a few years ago. and literally never have to buy a commercial antenna again, most likely.
Consider a biquad. The basic biquad with reflector will give you around 6-7 dbi gain but you can also make a double biquad which will give you "twice" that (3 db more) Basically it depends on what the pattern you want is, how wide
If you are determined to build a yagi, go for it but the matching part, the driven element, is the critical point. I would use a jpole like matching section, shape the driven element just like a j, with the feedpoint adjustable. There is where the nanovna2 would be useful because otherwise how do you determine the exact right spot to feed the Yagi? Depending on every little thing, that feed point may vary significantly. You would need to build or buy a directional coupler, a decent directional coupler is going to cost you, right there half of what the nanoVNA2 would cost you.
Wifi access points also don't have the power to work with a typical ham directional coupler. Ham SWR meters which might start at $20 used when you include shipping, (there are also some fairly decent new ones on ebay for not too much, which is cheaper than building them yourself because the cost of the magetic materials would put you uo there. ) are designed to work with ham equipment, not wifi equipment. You need something much more sophisticated to measure something without transmitting power that requires a license to do.
So you really cant lose buying one if you have any intention of making more antennas.