Can I use the 55w with this ballast?

No. This ballast is for Philips Cosmopolis White ceramic metal halide lamps, which works in a significantly different manner than an electronic SOX ballast.
Use SOX or fluorescent lamp ballasts only.

Indeed. That ballast puts out a 2.9kV ignition pulse as well, which would not do a SOX lamp any good at all.

Well the 2.9kV itself won't be any problem, but the limited OCV after this pulse ends (high pressure lamps suffice with 200..250V, most SOX need >300V to allow proper electrode warmup) will.
Plus not sure how the protection (lamp explosion prevention) features would respond to the SOX characteristics. It is very likely see it as an "EOL lamp" and shut it down.
All that assuming the rated arc voltages and currents somewhat match between those two lamp types (which I'm not sure either, I would see that as quite unlikely, but haven't checked).

The main problems are lamp voltage and current which are different in this ballast for the 55W SOX lamp, the operation at LF square wave operation, the high voltage pulse, and the EOL protection.

Damn, that's what the shop tried to sell me because they have the lamp but not the control gear. Maybe they don't care if the lamp die within a few months lmao. They do send me the photo of the lamp running with that control gear though.

OK - I just got a Fulham WH5 which some members have reported using successfully with the SOX 55w lamps, using just 2 of the 4 red wires, about $30. I'll be testing that soon. But someone else said that that ballast was underdriving the 55w a bit.

I first tested my 55w with the Fulham WH3 (both reds) based on a YouTube I found for putting together a fixture, but pretty sure that is too dim. The WH3 seems very good for SOX 35w though, as others here have also said.

Looking at the Fulham wiring charts for the WH33 and WH5, I see that the WH33 & WH5 (3 reds each) are listed for 1xF48 HO tubes, but only the WH5 is listed (3 reds) for the 1xF60.

So I'm thinking the WH33 (3 reds) should drive the SOX > WH5 (2 reds) and < WH5 (3 reds). But that doesn't seem linear based on rated wattage, since the WH33 is rated at max 64W (4 reds), and the WH5 is rated 128W (4 reds). Maybe WH5 (3 reds) would be OK with SOX 90w? But the YouTube guy recommended just 2 reds for that ballast. Probably underdriven, if the 55w is already a bit cool that way.

Has anyone tried a WH33 with SOX lamps? Inquiring minds want to know!

Or you could test with the more costy WH8. Since that's got 6 reds, to drive up to 6x T8F32 tubes, you would at least have more chances to find the optimum. Better odds than the slots, anyway!