I don't have concrete numbers, but from testing *other* things (namely, how to trigger an AI surrender before the diplomacy updates- note that I'm not and haven't been an official tester), I have witnessed that a shielded planet with high values in all regards (from troops to suitability), critically including the Planetary Bastion, can effectively negate low-grade mass bombardment.
Massive dedicated mass driver fire, including heavy cannons, pounding nearly harmlessly upon a well fortified Haakonish world. This is not how its supposed to be, and is due to a hardware limitation bug from a less optimized version. In other words, this happened because the galaxy was making the processor chug so much that it didn't compute correctly. In this situation where the above snip was taken, the Haakonish capital world fell to nearly identical fire within moments, while this world persisted through 10 years of bombardment.
However, most of the time (supposed to be all the time), they're a minor barrier to fire of any kind to a real battle fleet. Think of it like a modest little hit point pool with some mitigation, just like a normal ship shield. It will help against a small strike force with some dedicated bombardment weapons, but generally they're not effective because the only worlds you would build it on should have other defenses that will assertively stop such a small strike force. The way I'm guessing it calculates it is like this:
An attack hits the world.
Calculates what on the world it hits: troop, population, suitability, leader, or facility.
If there is a shield active, damage is mitigated.
If there is a shield active, chance and amount of damage bypass is calculated and then subtracted from incoming damage if successful.
The shield, if active, (not the facility) takes remaining damage.
Target on planet takes bypassed, mitigated damage (very small amount, if any, shield facility not immune to this).
If the shield is overcome or the shield facility is damaged, the shield is disabled.
If there is no active shield, target takes unmitigated, normal damage.
This is very similar to how ships damage is calculated (that process is certainly known from dev outreach). The screenshot scenario is the same thing that happens on individual ships that temporarily become immune to damage when their shields drop and armor doesn't take damage while taking lots of shots. On an overloaded processor, the shield status can effectively be semi-permanently active, absorbing damage as though it had much HP- even when completely reduced to 0- because incoming shots will still register that the shield is active, and the facility can be fully repaired before the processor catches up and subsequent checks on the shield status will see it as active. In other words, the 0 HP shields continue taking hits but doesn't go to negative values, the shield status doesn't update to disabled on other damage calculations, and in the next 'tic' the shields get their regeneration applied to a small value, the shield facility is repaired, and the subsequent round of incoming damage all registers the shield as active.
Most of the time, though, the calculation works fine and fleets punch through shields in short order.
Planetary weapons have been buffed significantly, but I still think they're not impactful enough to warrant building, let alone building a shield to help their already good durability. Their accuracy is still too low, though they seemingly unleash massive volleys. I've seen them destroy a ship here and there, and I assume that they're far more effective in the simulation (off screen). That, however, is another discussion.
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