Greetings.
I've recently tested in my HP Mini 110-3712la and actually the Realtek RTL8188CE works flawlessly in my Parabola GNU/Linux-libre installation with the linux-libre kernel version 5.9.12.
The results of the lspci -vnnnk are the following:
01:00.0 Network controller [0280]: Realtek Semiconductor Co., Ltd. RTL8188CE 802.11b/g/n WiFi Adapter [10ec:8176] (rev 01)
Subsystem: Hewlett-Packard Company Device [103c:1629]
Flags: bus master, fast devsel, latency 0, IRQ 16
I/O ports at 3000 [size=256]
Memory at 95000000 (64-bit, non-prefetchable) [size=16K]
Capabilities: [40] Power Management version 3
Capabilities: [50] MSI: Enable- Count=1/1 Maskable- 64bit+
Capabilities: [70] Express Endpoint, MSI 00
Capabilities: [100] Advanced Error Reporting
Capabilities: [140] Virtual Channel
Capabilities: [160] Device Serial Number 01-91-81-fe-ff-4c-e0-00
Kernel driver in use: rtl8192ce
Kernel modules: rtl8192ce
The results were the same with Trisquel 9.0 "Etiona" with the version 4.15.0-128 and PureOS with the kernel version 4.19.146.