All of the power supplies I have ever seen or used support both CC+CV modes. They taper off and stop exactly like the three steps you listed.
I used the Wanptek 60v model, based on a recommendation from someone I trusted who had taken one apart and examined its innards and found it to be of good quality, but two of the three I bought have since died. If you look at their advertising, they do not specify CC+CV mode support, but it was built in and you can see the little lights on the display that will switch on their own from CC to CV as voltage approaches the set target. Still, I don't recommend them given their long term unreliability.
Thats no mistake, the charger was really set to charge at 0.20a. This was a pic to establish a baseline while I timed the charge to see how much voltage was added in an hour at that charge rate. From doing stuff like that I was able to figure out the slowest charge rate for a routine down time.
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What I do recommend are the Mean Wells, which are in wide use as probably the best quality 'smart charger' you can lay your hands on in the marketplace. That includes the Cycle Satiator, which itself is effectively a tarted up CC+CV LED power supply, that has had a brain added with a GUI to set, store and select multiple profiles. The thing is the Mean Wells are a bit simpler, more durable and a lot cheaper.
How about a charger – quickly adjustable for voltage and current – that is rated for hundreds of thousands of hours of use before it typically fails?
talesontwowheels.com
^^^ I wrote that in 2019, had been using the Mean Wells for at least a year at that point and since then still no failures.