Is there a left-sided powermeter that requires less than 8 millimeters of clearance?

The Checkpoint is a gravel frame, and that particular model has a road groupset. Unfortunately, while not all gravel frames have this clearance problem, this does illustrate part of the rational for the slightly wider chainline on gravel-specific groups.

I would strongly urge you not to get a right-sided power meter based on a Shimano crankarm. It's been shown that because of the way the spider is shaped asymmetrically, drive-side meters on the current generation of Shimano cranksets (e.g. R7000, R8000, R9100) are inaccurate. The problem is not present on the non-drive side, but that's the side you don't have space for.

Given that and your cost limitations, it may be difficult to get a new functioning power meter within your budget. The lowest cost pedal-based meter that I know of is IQ2, but they are not yet shipping widely, they had to redesign their product completely once, and they have had numerous production delays. See my comment on your main question. A good crank-based solution would very likely involve a new bottom bracket, since many of these use 30mm spindles, and your Shimano group is based around a 24mm spindle. (An exception: Rotor makes some cranks with 24mm spindles, and Power2Max sells power meters with Rotor cranks, but these tend to be expensive and may be out of your total budget.) You could also try looking for a used power meter; to my knowledge, drive-side power meters based on the last generation of Shimano cranks are still reasonably accurate (see the GP Lama post that I linked earlier).

Used power meters are worth considering, but I would investigage the reliability history of the particular model if possible. To my memory, the second generation of the Stages units and the second generation of Garmin's Vector power meter pedals (neither of which apply to you, unfortunately; the Vectors are Look road pedals) were less reliable than their successors. Quarq spider-based units have generally been very reliable, but DZeros made before about 2018 could, in some cases, get irreparably damaged if they were subjected to a side strike, such as from a dropped chain (I was one of the victims on that thread). Quarq covered those of us under warranty for that failure mode, but you would not have this recourse. I had neglected to mention this earlier, but Powertap appears to have offered a disc brake power meter hub. You would be locked in to the rim it comes with, unless you chose to replace it, and you would want to verify that the hub either has a thru axle fitting or that SRAM (which owns and has now discontinued Powertap) or a dealer is willing to sell you the thru axle endcaps.

Train without power?

One thought is that you could do without a power meter. It's true that structured training with power can enable pretty substantial gains, but it also takes time and effort to select, learn, and adhere to a structured training regimen. Moreover, in the absence of a power meter, you can do unstructured but purposeful training. Ned Overend described this approach in the first part of this Velonews podcast. He tracked his time on various known segments, e.g. climbs, and he just made sure to do a variety of efforts of various durations, plus get enough rest. You can use Strava for tracking segment times, and it will also estimate your power in the absence of a power meter (making a large number of simplifying assumptions, so it's not a substitute for real power, but it is actually reasonably accurate on average). Hence, you'll only need a GPS head unit, which you would have needed for your power meter anyway. The term I used earlier is not a formal term, and I don't believe there's one for it. It's a bit more structured than the advice "ride lots", a quote from Eddy Merckx when asked about what advice he'd give to aspiring riders. This approach is perhaps akin to fartlek workouts in running.

You could also train with heart rate. When you do decide to upgrade to power, many structured programs also incorporate heart rate data to gauge your freshness, so a heart rate monitor purchase wouldn't be wasted. For example, Strava will display freshness information to premium subscribers, and that requires either heart rate or for you to enter perceived exertion on every ride. For heart rate, one thing to know is that it's a lagging indicator of effort. Once you start a hard interval, it takes your heart several seconds to catch up. It's not as good for short hard intervals. And heart rate is also influenced by fatigue, so you still need to listen to your body; if you are having a hard time getting into the prescribed heart rate zone, you may want to take an easy day (but that principle also applies to power-based training). It's likely that heart rate is better for longer duration intervals. However, if you are riding gravel, those are the type of intervals you want to concentrate on. You could supplement longer intervals with shorter, unstructured sprints, or do an occasional day of short hill repeats to get your top end speed built up.