I agree with the flinch/suppression mechanic, it should be increased across the board, not just snipers.
I do not agree that a 6.5, .308, .338, .50 sniper round or whatever they are including in BF6 should be anything but a 1 shot kill. That's ridiculous.
If the current aiming for snipers is hit/scan take that away and make it a projectile again with bullet drop like previous battlefields which will make it more difficult to hit a moving target.
Remove the glint or greatly reduce as others have said so that you have to be actually looking down sights at the direction of the sniper to see the glint. Add swirl, or a tracer. Anything to make it less obvious where the sniper is located, until they shoot. As a player, keep your head on a swivel and look for spots snipers might be hiding and use cover. Bring back the Bino's. Use smoke to cover your movements. Make the player counter the player, not some old fashioned unrealistic mechanic that baby's the player.
Perma-death kills should be expanded if anything to include rockets and tank rounds. There would not be much left to defibrillate.
I'm old, I started playing back in the battlefield 2 days on LANs, have more hours than I'll admit here logged on BF3/4 on Xbox. Played BF one, 5, 2042. My experience with rush/breakthrough has never been that snipers are OP, that they dominate or that everyone in the lobby is a sniper, your experience is probably the exception. Snipers should be a force multiplier, so a few decent snipers may feel like an entire teams worth. Truly the king of Rush/domination is a well coordinated tank/engineer crew. They will always dominate an un coordinated defense or offensive team. What is the counter? you guessed it... snipers taking out the engineers while they repair.
We played several games of breakthrough as offense where the tank driver and gunner went 70+kills with ~4 deaths with a win. No one could kill our engineers because the driver played smart, hung back and we took out the glinting sniper and their squads with ease. That is not to suggest that tanks are somehow OP, but team work should always be the path to victory and its nice that the HMGs on the tank do not feel like a nerf gun this battlefield. I was impressed with one OG who brought back the VB-IED C4 buggy, taking out our tank on the final push, killing us all and wining the match for his team. Played plenty as defender where the tank crew was not coordinated and easily knocked out by infantry as well, seems balanced enough.
When the game releases there will hopefully be plenty of gadgets to counter snipers again, vehicles aside. Mortars, drones, laser designators, guided munitions etc I'm hoping make a return. Its also extremely difficult to win as offense if your entire team is made up of snipers, who would actually push the objective? Defending snipers should be feared and have the advantage over assaulting snipers by nature. There are other game modes/maps where snipers are dominated by CQB classes or are less effective because of vehicles.
I don't think the controller/keyboard mouse complaint is anything new or that can be fixed for a cross platform game. Other than to let everyone on every platform use whatever preferred input they want. It certainly doesn't specifically benefit snipers over every other weapon type with the recoil management and targeting speed of a mouse.
Have gadgets, weapons, perks, vehicles that promote and incentivize teamwork, people will find creative ways to counter everything. Don't expect to play each map/type the same and win every game, especially solo.