I would suggest you wait a few weeks before making a decision, because there are strong rumors of two new Canon R-series cameras being announced at the end of this month (
https://www.canonrumors.com/). These are expected to be the first two APS-C R-series models, which will probably be called an R7 and an R10. The R7 will likely be a mirrorless version of 7D Mark II/90D... a more advanced and more expensive model. No one knows all that much about what to expect in the R10, but it's generally thought it will be a more affordable, somewhat lower specification model. Perhaps a "mirrorless Rebel" or a replacement for the M50 Mark II?
The R you're considering is full frame and the oldest of the R-series models... the first of that series they introduced. It's 30MP and isn't bad, but also doesn't enjoy a lot of the nifty autofocus advancements Canon has put into the more recent (and more expensive) R6, R5 and R3. Before committing to it, I highly suggest you review some of the YouTube video reviews of the R and its AF system (as well as compare to the AF systems in the later models).
I am pretty sure you will find the a6600's AF system superior to the Canon R's... HOWEVER,
not with adapted Canon EF/EF-S mount lenses! You'll only get full benefit of the a6600's AF capabilities if you ditch those Canon lenses and replace them all with Sony lenses. While it's possible to adapt Canon lenses for use on Sony cameras, there is some loss of autofocus performance doing so.
There IS NOT any loss of performance adapting those Canon lenses for use on the Canon R-series cameras. In fact, some users report their adapted EF/EF-S lenses work better than ever when adapted to the RF-mount. It is a pretty good bet that the upcoming APS-C R-series models will benefit from the improved AF performance too... both with native RF lenses and with adapted EF/EF-S lenses. In fact they should make even better use of EF-S lenses than the full frame R-series can.
This is especially true with IS lenses when they're used on the later R-series cameras that also have IBIS, where the two stabilizing systems work together for increased effectiveness. Speaking of which, that's another difference: The Canon R doesn't have in-body image stabilization (neither does the cheaper RP). The a6600 does have IBIS. As do the later Canon R6, R5 and R3. It's also expected that the upcoming R7 will have IBIS. But it is NOT listed as one of the "leaked" specs of the R10. So we're in wait-and-see mode with that camera.
Right now it's anyone's guess how much the R7 and R10 will cost. I would predict (hope?) the R7 might be around $2000. Less would be great! But the 7D Mark II was introduced at $1800 in 2014 (sold for as low as $1500 before being discontinued), while the lower spec 90D was intro'd in 2019 for $1300 and is now selling for $1200 (all prices are body-only and US $ per B&H Photo). In some ways the specs of the R7 follow those of the 7DII (dual memory card slots, for example), but in other ways it sounds more like a mirrorless 90D (32.5MP sensor).
The R10 should be close to $1000 or maybe even below that, if it's significantly lower specification. The Canon M50 Mark II is selling right now for about $600 US, the M6 Mark II for $850. The Rebel T8i is selling for $750 and the Rebel SL3 for $650. So it sort of depends upon what the R10 is intended to replace: Rebel DSLRs or one or the other of the M-series mirrorless.
It's possible the R7 will be the same size as R6 and R5 full frame models. This was the case with the 7D-series vs the 5D-series cameras. One possible advantage would be that the new APS-C camera could use the same BG-R10 battery grip as the two full frame cameras. Another advantage is room for dual memory card slots and a larger battery. Now the R6 & R5 are smaller than comparable full frame DSLRs... so you could hope the R7 will be smaller and lighter than the 7DII, as well. However, probably not as small and light as the Sony a6600.
The R10 might be smaller, depending upon the format it follows. A really inexpensive version might not even have a built-in viewfinder (but may have ability to use a separate, accessory EVF like the M6 Mark II can do). If it's scaled to the M-series cameras or smaller Rebel like the SL3, it could well be close to the size and weight of the a6600.
Based upon what you say you like to shoot... "people, sports, wildlife and flowers are my main subjects"... and appear to want to keep prices reasonable, size and weight to a minimum, in my opinion an APS-C camera is your best bet (be it a Canon or a Sony). Especially for subjects like sports and wildlife that often demand fairly powerful telephotos, an APS-C sensor format provides significant advantages. It makes smaller, lighter, more affordable telephoto lenses "more powerful".
However, be a little careful about "too small" a camera. I do a lot of sports and a little wildlife photography, using a number of fairly hefty telephotos. I choose moderate size cameras because they balance better with those lenses. I even fit grips with dual batteries, which increase the weight and mass of the camera. I have a small APS-C mirrorless, but I don't use it with those bigger telephotos. That camera is just too small and light for comfortable handling with even 3 or 4 lb. lenses... and would be absurd with 6 and 8 lb. "super" telephotos! (Canon appears to agree with this... the longest focal lengths they sell for their small M-series are compact 18-150mm and 55-200mm zooms.)
I'm waiting to see what Canon announces at the end of this month. Depending upon what Canon comes out with, I might replace my APS-C DSLRs (two Canon 7DII backed up by a pair of 7D).
My very small, compact mirrorless (Canon M5) with four small, unobtrusive lenses will probably continue to serve for candid portraiture and street photography... as well as travel/hiking/biking when I want to keep things as light as possible.
I have and prefer using a full frame Canon DSLR for formal portraiture and for macro work. FF is also my preference for landscapes, architecture, though I don't currently do very much of either. I'd also choose FF if I were a wedding or advertising photographer, but I'm neither.
I'm not saying FF isn't great when size, weight and cost aren't a concern. Heck, for some things I might even consider medium format digital if that were the case!
But if I could only have one camera I'd choose an APS-C because it can handle all these purposes very well and has distinct advantages in some of my main purposes (and I'd rather spend my money on lenses than on the cameras behind them).
It sound like we'll have some new options from Canon in a few weeks! I'd suggest you wait and see what they announce.
I would suggest you wait a few weeks before making... (