It will work. Just mind the volume and listen for signs of speaker distress if you crank it up. There's nothing electronically incompatible. Note that Ampeg lists 500W power handling in the specifications for the SVT-410HE. Should be fine... Use your ears.
@MJBoult apparently has one of the older 1990's HE cabs, which are only rated 200w (4 Ohm speakers rated @ 50w each for that cab, 2 wired in series & then the pairs in parallel for the 8 Ohm load I
suspect:
https://www.talkbass.com/threads/ampeg-svt-410he-older-200-watt-version.1569300/ ). The current ones are 4 x 32 Ohm speakers in parallel = 8 Ohms according to the Ampeg wiring diagram (and with higher rated speakers for 500w rms total).
For home use or with a jazz trio you can use your ears,
personally for a harder rock trio+ and loud drummer, I would not trust my ears with a 8 ohm 200w cab + the STM-900 ... but that is just [overcautious]
me. The STM-900 puts out 500w into an 8 ohm load, has a lot of low end on tap and is often especially loved for its possible [boosted] hair.... unless the band is very disciplined & quite, 200w can be easily exceeded to keep up, more so if some grind and boosted low end on the Streamliner is dialed in....
If the speakers are 4 Ohm & the old HE cab were to be re-wired (easily) internally [and label it as such

] to have the 4 x 4 Ohm speakers in series = 16 Ohm, it would be a much closer/safer match for an STM-900 (amp = ~300w amp output @ 16 Ohms... still over the cab rating, but
much closer)...
I rewired my NeoX 212Ts (stock 4 ohms = 2 x 8 Ohms in parallel, rated 600w rms per cab) internally to series for 16 Ohms for my Streamliner 900, one for the band practice room use (~300w amp output) and two for gigs (= 500w amp output @ 8 Ohms with the 2 x 16 Ohm cabs connected to the amp in parallel) when needed. Harder Rock/Punk/Metal & two gain happy guitarist to deal with in the mix here. You can also push the Streamliner output stage into output tube emulation this way at lower volumes as an added bonus if you wish: see
https://www.talkbass.com/threads/ran-my-streamliner-at-16-ohms-tonight-a-revelation.1333627/
Even with 16 ohms, still keep an ear open... an STM-600 would be a perfect match with a 200w 16 Ohm cab (~200w amp output @ 16 Ohms and be able to add up to a ridiculous 3 x 16 Ohm cabs in parallel as needed to go higher up to the 4 Ohm minimum amp rating... ).