Fuses are a completely separate topic.
Power supplies and DC-DC converters just keep putting out current until they are turned off, either manually or by an HVC circuit.
Ancient garage-style chargers used to be the same, basically obsolete.
Proper chargers these days all have a stop-charge algorithm for safety and to prevent overcharging the battery. Dropping to a lower Float stage voltage after the bank is full is as "smart" as is needed, aka 3-stage charger.
More complexity and automation than that is rarely a good sign.
Really good ones, the user can custom adjust, not just the Absorb / CV voltage, but also how long Absorb is held.
Looking at a few hundred bucks, but we'd need to know more detail to make specific reco's.
Type of battery, specific make & model and Ah capacity? (ideally a link)
Different types you may want in future when replacing the current ones?
Used for what purpose?
How fast do you need to charge?
What specs on the mains supply circuit?