@dobey I have filtered https connections for years without breaking the encryption, this is easy when the proxy is declared in the browser (non transparent proxy).
What I want to do now is the same thing inside a smartphone running UT, to be able to filter Internet connections. So this is really an UT question because the proxy will be running inside the phone, I cannot have any control of connections running through 3G or 4G.
I have already installed UT on my Nexus 5. I have already set up the filter with an internal DNS server (Unbound) and it works. But filtering with squid is slightly better and I would like to test it.
@arubislander : thanks for the suggestion. But it is not a possible solution because if the proxy is not declared in the browser, the browser will encrypt itself the connection, and filtering is no longer possible. If the proxy is declared, the browser communicates with it without encryption (otherwise the proxy would be unable to do its job) and the proxy encrypts the connection if it does not have the page in cache and must forward the request.

I installed Ubuntu Touch on a Nexus 5. Everything I tested is working fine. Internet connection by WiFi is OK. The problem is that the SIM card is not detected. Googling a lot came to a possible answer :
https://forum.xda-developers.com/ubuntu-touch/help/sim-detected-nexus-5-t2858419
Which says :
Solved thanks to a script in /usr/share/ofono/scripts/ which is "enter-pin"
So, try typing in a terminal ("xxxx" is your pin code):

/usr/share/ofono/scripts/enter-pin pin xxxx

I tried it but got an error :

phablet@ubuntu-phablet:~$ /usr/share/ofono/scripts/enter-pin pin 0000
Enter Pin for modem /ril_0...
Traceback (most recent call last):
  File "/usr/share/ofono/scripts/enter-pin", line 27, in <module>
    simmanager.EnterPin(pin_type, pin)
  File "/usr/lib/python3/dist-packages/dbus/proxies.py", line 70, in __call__
    return self._proxy_method(*args, **keywords)
  File "/usr/lib/python3/dist-packages/dbus/proxies.py", line 145, in __call__
    **keywords)
  File "/usr/lib/python3/dist-packages/dbus/connection.py", line 651, in call_blocking
    message, timeout)
dbus.exceptions.DBusException: org.ofono.Error.InvalidFormat: Argument format is not recognized

I don't know what is the format error.
Otherwise, where can I enter the SIM pin code ?
I am locked there.
It could also be a hardware problem, I tried to reinsert the card several times, but no change.
Thanks for any idea.

I want to set a proxy in the Ubuntu Touch browser, Morph, so that queries can be filtered by squid. Setting squid as a transparent proxy does not make the job because https connections cannot be filtered like that.
I have been unable to find any information on that point. Does this require to patch the source code and rebuild ?
I am working on a Nexus 5.
Thanks for any information.

Update : I tested Onion browser, but I still don't see anything for giving a proxy IP and port.

@kugiigi thanks a lot for the answer. Knowing it is possible is important, thank you. I'll have a look at this.

I had the same issue and was highly disappointed to find a system so tightly locked. I want to add a feature, which implies manipulating nftables, unbound, vsftpd and things like that, if they are installed in a container, is there some hope it will function ?
I tried to remount the partition rw, but the space is strictly limited to 2GB, when I have 16 GB on a Nexus 5
I am used to Debian (Stretch and Buster).