WORK IN PROGRESS (Era, Orange and Plus aren't added yet)
All of them were downloaded from the Polish file hosting service Chomikuj.pl (Wikipedia).
The old version with Era and Plus wallpapers -> (click)
Era
(1996-2011)
Orange
(since 2005)
Plus
(since 1996)
Heyah
(since 2004)
The first wallpaper, in 128x160px resolution, was reuploaded multiple times from 2008 to 2013. It's the only one from this brand where I can confidently say is official.

The next four wallpapers in the resolutions 128x128px, 128x160px, 149x191px and 176x220px. They were uploaded to Chomikuj during the same time period, but only once or twice each.

Generally speaking, Heyah is a prepaid mobile brand originally marketed toward teenagers and young adults, known for its edgy ads. In 2022, it shifted its target audience to the Ukrainian minority in Poland.
T-Mobile
(since 2011)
Four GIFs available in two resolution sets: 128×160px and 240×320px. These were uploaded multiple times between 2010 and 2012.

Interestingly, they appeared on Chomikuj a year before the rebranding. In 2010, the network was still known as Era (one of Poland's major mobile brands during the 2000s) operated by Polska Telefonia Cyfrowa (Polish Digital Telephony). In 2010, the PTC was acquired by Deutsche Telekom, and in 2011, the Era brand was replaced by T-Mobile as part of an international brand unification. Later, in 2013, Polska Telefonia Cyfrowa was officially renamed to T-Mobile Polska S.A.
I still remember how my mom was unhappy with that change, because the new offer had worse terms of use (according to her), so she moved her number to Plus.

The images on the left were used as (non-looping) startup screens, while the ones on the right were probably screensavers.


Play
(since 2007)
After early network tests in 2006, Play entered a telecommunications market oligopolized by three main players: Era, Plus, and Orange. Thanks to an aggressive marketing campaign, better contract terms, and low call charges, they managed to become one of the main players on it, which is now oligopolized by four players: T-Mobile, Plus, Orange, and Play.

For the additional context, I have two comments posted under this Polish article:
When writing about Play, it's important to remember the higher Mobile Termination Rates fees that customers of other networks had to pay. For a long time, calling someone on Play was significantly more expensive than calling someone on Orange, Era (T-Mobile), or Plus. Meanwhile, Play offered the same rates to everyone. That's why many people switched to that network. (...) by Siara
---
When Play appeared, I switched to that network, tempted by simple, cheap offers without any catches. For 4 years I renewed my contracts because I was getting good terms, but unfortunately after some time Play became exactly like the competition, not cheap at all, with offers full of catches, and they stopped fighting to keep customers. That's when I left and I have no intention of going back. by Krzysztof Ł.

Two sets of four wallpapers in 176x220px an 240x320px respectively, uploaded a few times between 2009 and 2013.