US long term capital gains do work that way: they have marginal brackets just like regular income taxes. (Your starting bracket is calculated based on your regular income, rather than from 0 the way regular income tax brackets work, but otherwise they work the same.)
I assumed the discontinuity the commenter was referring to here is the >=1 year cutoff for long term capital gains. After one year, all of the gains from the previous year are instantly converted to a lower tax bracket. You're not required to reassess the cost basis at the 1 year mark or anything like that, so there's a huge (intentional) incentive to hold capital for over 1 year.
I can’t speak for all member states but I do know some have a threshold and from that point you have to pay a percentage of the total amount. So some investment firms will game your portfolio to bring you in just enough to fly under that threshold.
The U.K., while not technically an EU member any more (and I’m still bitter about that), also operates this way.
Stamp duty is a U.K. tax placed on purchases of property. It’s free for properties under a threshold but the moment you go over it you have to pay a percentage of the total price of your house. Stamp duty does have incremental percentages but it isn’t calculated like income tax. Thus you’ll often see a lot of properties for slightly under each increment and then a jump in prices after. Some sellers even go as far as to put the house on for £x (under that threshold) but charge extra for additional purchases outside of the property (like a gazebo, hot tub, etc). I’ve even seen some buyers/sellers ask for private bank transfers for the additional extra. Which is outright fraud. But it does still happen.
No. Income tax you only pay the percentage of the bracket you’re in. So (made up numbers here) if you earn 100k and the bracket changes every 40k then the first 40k will be taxed at the first bracket. The second 40k at the second bracket, and the remaining 20k at the third bracket. This means there’s no incentive to game income tax because if you narrowly slide into the next bracket then you only pay the higher tax rate for that margin you’ve gone over.
Whereas the capital gains and stamp duty go from (again made up numbers) 0% on 15k to 15% on anything above 15k. So if you had 15k you get taxed nothing. But if you get 15,001 then you pay 15% on ~15k (just by gaining an extra £1) rather than 15% on £1 (like how income tax works). Thus that extra £1 actually ends up costing you _a lot_ more in tax than it’s face value. And thus why people game such taxes to slide under the threshold in ways that doesn’t make sense with income tax.
There have been exceptions to that reform though. For example the “stamp duty holiday” incentive ~two years ago removed marginal bands for the lower thresholds during its run. Which created a great deal of chaos for the housing market.
And short term cap gains are just regular income.