Using the rear brake in the wrong place can and will upset the bike at track pace. On the road it's generally advocated as the safer option, and I've alternated between rear only (except in emergencies...) and front only on the road and prefer the feel of front end biased braking in most conditions, plus it means I can draw on my mountain biking experience / reflexes (which is relevant to a point, so get out there!)
In the game, using only the front brake means you can quickly learn the threshold of grip up to the point you low-side out of the corner (the feedback of applied braking force is lacking slightly, but keep at it). The tyre model is actually really forgiving, I've had several front end slides from locking up on the brakes in this game already that I was able to recover from, and you can hear it squeal. My real life experience tells me that a lock up at any angle of lean will very quickly drop the bike, and you'll be so very lucky to get it back if you weren't expecting it (unless you're off-road where front end skids are always happening).
Trail braking is very important on a bike in general for a few reasons (more front end grip, better tracing of ideal line by controlling speed etc.). Similar to a car, you have to reduce the force as you begin to turn, doubly since you are leaned over. This game is very forgiving in terms of how hard you can brake when leaned over at speed (as is real life if you have good technique, by keeping the tyres properly loaded), but less so as you slow down, meaning you are more likely to bin it nearer the apex.
Sort of contrary to the above advice, unless you lock it up, using the rear brake actually widens your line at a constant speed - this is partly because of the effect of the resulting change in geometry on each tyre's load (grip) and partly because of the turning moment of each tyre around the bike's C.o.G. relative to its inertia. It's the reduction in
speed that ultimately tightens your line, so doing it in a way that doesn't force you wide first is generally better.
In the ideal case, the front brake should be used to steer the bike into the corner, at least initially - this is because this is where the most grip is, certainly, but also it pitches the bike forward, sharpening the steering. If used alone, the rear brake, as I alluded to above, actually acts to compress the rear suspension, limiting load transfer to the front wheel. Some riders habitually scrub the front brake just before turn in, even if they don't need to slow down, because of how it affects front end feel.
In very fast sweeping corners, or just generally with bikes of low power where corner speed is paramount, using both brakes very slightly is the best way to scrub speed into a corner. Using this technique means you make best use of available grip at both ends to keep corner speeds high especially near the apex, whereas using just one brake might overwhelm that tyre and you will either slide or be forced to take the corner slower overall to avoid it.
This is very hard to do in the game because of the controls layout and lack of analogue rear brake by default (I use R2 / RT, as recommended by another member here, and the right stick for throttle / front brake). It's also very hard to do in real life, which is why racers in the low capacity classes still get a lot of respect, and why many of them can never transition successfully to "big bikes" due to the different corner entry style (stop, turn, squirt: the V shape) - as well as the profound chassis effects caused by all that power.
I'm not quite up to speed with the controls in the new game, and I currently mainly use the rear brake when I've run deep and have no more front end grip to exploit, and I am indeed actually trying to skid the rear around slightly. Sliding of any kind is more advanced and more likely to have you off the machine, so it's best to stick to learning speed control in all parts of a corner first, keeping it simple before pushing the envelope.
In the wet, where low grip levels limit the deceleration rate, the bias of grip front-to-rear during deceleration (load transfer) is not as great and the rear brake is more useful in general stopping duties - however, this should also be considered advanced technique in terms of your control inputs if using split brakes.
In the dry, I think the anti-stoppie control in the game makes the rear brake more effective in a straight line than it should be.
Some possibly helpful stuff on Wikipedia
here.
Bear in mind engine braking has a huge effect, being applied only to the rear wheel - hence slipper clutches and tuneable engine braking strength on modern bikes.
What I used to do in RIDE 2 was brake very hard using both brakes for the straight-line portion, then release the rear and feather the front as I turn in. From there, continually and gradually bleeding off braking power (observing how quickly my line is tightening). Finally, I feed in a very slight amount of rear brake again (with the front still on, as above) to sort of plant the bike on the apex. Some bikes did not like the use of rear brake during the hard braking phase, tending to lose stability or slide wide on turn in, so I adjusted my style accordingly.
The hard part is balancing all of this with the steering, because it's very easy to turn in too early or too late and not match your speed for the effective corner radius as it changes along the racing line through a corner. Luckily, thanks to their narrowness and their relative power, bikes can exploit any of many racing lines in most corners without too much penalty (gifting overtaking opportunities notwithstanding).
Depending on the corner, you may want to have picked up a neutral throttle (never coast off-throttle; again, it slows the steering down and pushes you wide) before the apex or just as you hit it, but typically there will be some element of waiting for the bike to turn before you begin to fully open her up - on all but the most powerful of machines, or in certain hairpins, this waiting on a smooth line actually means you've got it right.
One exercise for training this sense is to use the throttle to steer: rolling on the throttle pushes you wide, feather (don't chop) it off to tuck in again. Cadwell Park's Chris Corner is a great place to practice this on a 300 class machine - tip in, meet the "apex" at the curb: wait on a neutral throttle; then feed it in and gradually use all of the track's width. Trail braking is very much similar in terms of its ability to alter your trajectory and you can use it to control your line in a similar way: more (light) braking tightens the line; no braking, no throttle will run you deeper / wider. The entry to the Gooseneck chicane, after Chris Curve, is a great place to practice that. Then try it on a 600, where those two corners become one.