Intro

I build a few wireless keyboards by now, and those are the 3 ways I mounted my batteries, all with their own upsides and downsides.

Underneath the MCU

Most wireless builds out there socket the controller. Those sockets add some height to the controller.

This gained space underneath the MCU is perfect for small 100 - 150mAh batteries.

Battery underneath MCU
https://www.reddit.com/r/crkbd/comments/lz74s2/first_nicenano_build/
Batteries & MCU socket
Batteries & MCU socket

anything with roughly 12x30x3mm

110mAh & Mill Max socket

Drawback:
Small battery capacity

Above the MCU

A lot of keyboards cover the controller with acrylic covers, sometimes for an OLED, sometimes just for some protection.

It's possible to replace the default standoffs with larger ones, which means we can mount rather thick batteries there.
Use some double-sided tape to secure the battery to the acrylic cover, that way it'll stay in play during normal use.

Battery mounted on top of the MCU
Taped battery & cover to make it less hideous

They'll do the job at home, but I wouldn't dare throwing such a keyboard in a backpack.
Those acrylic covers snap very easily at the screw holes, raising them for battery clearance isn't helping that.

That being said, having batteries last multiple months instead of a few weeks certainly is appealing.

The 1100mAh batteries on my Lily58 were mounted that way, and it worked just fine. Only recharged those once after around 3 months, soon after that I moved on to a Microdox.

Batteries
Batteries

anything with the footprint of an MCU

1100mAh batteries

Drawback:
Not very sturdy if you travel with your keyboard

Between PCB and bottom plate

A lot of split keyboard cases are just two plates, the switch plate and the bottom plate, screwed together with some standoffs.

With MX switches, there is usually very little space left between the PCB and bottom plate.
But Chocs don't have the 2mm between the top plate and PCB, thus gaining those 2mm between the PCB and bottom plate.

Battery sandwiched
2-4mm batteries will fit just fine

This doesn't mean we can't use this mounting style with MX switches, we just need to use longer standoffs.

The batteries can't be very thick, but there are very little restrictions otherwise.
All the unused space between the PCB and bottom plate is battery space.

Batteries in a Microdox Bud case
Even managed to fit that battery into a Microdox Bud

Drawback:
Spicy pillows are dangerous

I've been using such a setup on my Microdox for about a year now.
The battery is 4.1mm thick and I measured 4.4mm between the PCB and bottom plate. It still slides around a bit, but if the battery was on the thicker side (product page said 4mm +-.5mm) it could get dicey.

It may be advisable to get some slightly longer standoffs and use double-sided tape to secure the battery, instead of squishing the battery between the PCB and bottom plate.

Batteries
Batteries

anything with longer standoffs

830mAh batteries

Comparison

underneath above between
Battery life ~2 weeks ~3 months ~2 months
Low Profile MX doesn't change only adds to the top raises the whole keyboard
Low Profile Choc doesn't change only adds to the top doesn't change
Optics pretty much hidden very visible hidden

Battery life are based on my usage, with the mentioned battery sizes and no additional features.
Wireless keyboards with RGB and/or OLED will draw significantly more power.