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I would like to know what is the battery life cycle of a Magic Mouse 2. Or the approximate number of charge/recharge cycles before its battery's performances will start to reduce visibly?

The Magic Mouse 2 uses a lithium ion battery and generally speaking those have a useful life of 3 to 5 years¹.

That said, it's important to note that:

• Apple products (including accessories) have a 1 year warranty


• Only accessories included with a Mac computer are covered under AppleCare. In other words, if you buy AppleCare for your iMac that includes the Magic Mouse, it's covered. It won't cover it if you bought the mouse separately (like with a MacBook)

From personal experience, I've had rechargeable batteries in a Logitech Mouse last the better part of a decade and brand new batteries (genuine OEM) from Dell and Apple fail after a year. YMMV. (your mileage may vary)

¹Manufacturers' information typically specify lifespan in terms of the number of cycles (e.g., capacity dropping linearly to 80% over 500 cycles), with no mention of chronological age.[162] On average, lifetimes consist of 1000 cycles,[163] although battery performance is rarely specified for more than 500 cycles. This means that batteries of mobile phones, or other hand-held devices in daily use, are not expected to last longer than three years. Some batteries based on carbon anodes offer more than 10,000 cycles.[164]

Lithium ion battery life is specified by manufacturers in number of CYCLES, that translates in 3-5 Years.

The 3 to 5 Yr a very large gap. WHY?

The reason for it is because the life span depends on USAGE.

Degradation

Over their lifespan, batteries degrade progressively with reduced
capacity, cycle life, and safety due to chemical changes to the
electrodes. Capacity loss/fade is expressed as a percentage of initial
capacity after a number of cycles (e.g., 30% loss after 1,000 cycles).
Fade can be separated into calendar loss and cycling loss. Calendar
loss results from the passage of time and is measured from the maximum
state of charge. Cycling loss is due to usage and depends on both the
maximum state of charge and the depth of discharge.[95] Increased rate
of self-discharge can be an indicator of internal short-circuit.[165]

Degradation is strongly temperature-dependent, with a minimal
degradation around 25°C, i.e., increasing if stored or used at above
or below 25 °C.[166] High charge levels and elevated temperatures
(whether from charging or ambient air) hasten capacity loss.[167]
Carbon anodes generate heat when in use. Batteries may be refrigerated
to reduce temperature effects.