I believe there is a very simple solution that I am surprised was not implemented already, but first, let's outline the issue:
I played three matches of Planetary Supremacy (Henceforth referred to as PS) against the exact same army, wielding the exact three same units, just in varying number. I now have 0 interest in starting a PS campaign as the other races and little desire to continue my necron campaign.
Easy solution - a myriad of randomly selected "themed" encounters. Some examples:
A 1000/1500 point regiment of Death Company being led by a chaplain trying to find them an honourable death.
A 500/1000 point Death Company chaplain-less that had to be abandoned due to heavy BA losses.
A Necron force that has went mad with the ravages of time, awakening not under control of the main force.
A collection of Tyranids without a synapse creature to lead them - could be a true horde.
A small Tyranid force led by a synapse creature that has lost connection to the Hivemind.
A forgotten mausoleum that houses a number of mad dreadnoughts.
Etc Etc
There would be a small pop-up of text (likely where it normally shows enemy race and rewards) detailing what the encounter is and why they are separate from their respective race.
I would even advise having a campaign modifying check-box that allows for mirror matches, it wouldn't take much to justify an inter-race conflict as many of my examples demonstrate - making it optional would allow those that are much more lore-strict to remain happy whilst providing an entirely new match-up for each race.
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The previous text is separated as it simply uses in game assets and requires the least possible amount of work to address the lack of diversity in PS and would go a long way in addressing what currently feels very stale.
The next solution would require more work as I also suggest having recolours of the races as Sub-factions of BA, other Dynasties of Necrons and different Hive Fleets. To actually differentiate them between the OG in-game races i would advise having the armies strictly follow their themes: Hive Fleet Gorgon focusing a list around Venomthropes as they are heavily poison themed, I actually found a summary of the Hive Fleet differences as listed in an older codex that I will copy below, I believe it illustrates my point that a specific style of list could be tailored around the sub-faction themes.
I would again advise an optional toggle for those that want closer to the lore of the Devastation of Baal.
This is a complete wall of text that I do hope is taken as the constructive criticism it is intended to be. Battlesector is likely the closest GW will ever allow a game to come to a digital replication of tabletop (something I have long since dreamed of) and I would hate to see this uncut gem left in the dust due to lack of profit. I eagerly await any updates to PS and the game as a whole and wish you ever success going forward.
Behemoth - Overwhelming force, swarms of small creatures screening for a core of monstrous creatures like carnifexes and bio-titans.
Kraken - Attack from many angles, defenders crippled by genestealer cults, weak points surgically destroyed.
Leviathan - Physically the largest fleet on record. Highly adaptable strains and strategies, highly coordinated and long-range hive mind, even for Tyranids.
Gorgon - Specializes in chemical and bio-warfare with customized toxins and viruses used to soften up or outright depopulate worlds they target.
Hydra - What appears to be a rogue fleet that turns up to feast on defeated tyranid invasion remains, and then start where the last one left off. Focuses on huge swarms of small creatures by seeding planets with spores prior to invasion.
Jormungandr - Infests asteroids and then hurls the asteroids at the target planet. The few that survive the orbital defenses and the impact get stuck in and begin to reproduce and establish lairs in the planet's crust. Built for slow, grinding attrition warfare, nearly impossible to permanently root out.
Kronos - A small splinter fleet that appears to have been grown specifically to fight chaos. Eats worlds that other hive fleets deliberately leave defenseless but undigested. Focus on long-range and artillery combat, since chaos-infected matter can't be digested by the hive fleet. Extremely strong shadow in the warp, making it difficult or impossible for psykers, sorcerers, and demons to operate near them.
Tiamet - Mentioned elsewhere in this thread. Don't actually eat worlds. Instead, they turned up in the Tiamet sector, crushed all resistance, and then got stuck in guarding some continent-sized psychic tyranid construct. On an individual level, they grow resilient and tough, harder to kill than similar breeds of other fleets.
Ouroboros - Believed to be the leftovers from an ancient hive fleet from long before the "first" recorded appearance of hive fleet Behemoth, matching ancient legends of monsters from early in the Imperium's life. They feature primitive versions of other hive fleet's creatures, and on a tactical level field a lot more flyers than other fleets.
