I should also point out probes have there own voltage ratings, looking on the side of a random one I have on hand (X1: 150V, X10: 300V) its not a siglent probe, so check yours first.
If the probe cannot handle the voltage, but the scope can, it means you will just have to use a coax cable to measure it.
Siglent example PP510 and PP215 and PB470
10x 600VDC (or AC peak)
1x 300VDC (or AC peak)
Just checked one of my siglent PP510 probes and it says this on the probe itself:
1x 150V
10x 300V
CAT II
user guide for that probe says:
max input voltage: 1X:150V RMS CAT II&10X:300V RMS CAT II
You are right.
I chek PP215 and PB470 from real probe in my hand.
PP510 I check from Siglent list what I have get from Siglent and it say:
PP510 1X/10X attenuation, 85/18pf, 1M/10Mohm, 6M/100MHz, 300V/600V,
operating temperature -15 to 75 degrees
Same as PB470 and PP215 exept bandwidth.
Now I open one scope carton and take PP510 my hand and..... ....and it is just as you told 150/300V.
Except...
PP215 is 300/600V DC and PK AC
PP510 probe read 1x 150V 10x 300V CAT II and nothing more
but in probe pouch small sheet reads
1x 150V RMS, 10x 300V RMS
Ok if I think 300V AC RMS. Then Vpk is 424V rounded 400Vpk.
But then, what is AC without frequency. Oh yes, one mHz and uHz is also AC. All except theoretical DC is AC. And it do not exist in nature. So, only conclusion is that it can also turn to 300V AC RMS, 400Vpk, 400V "DC".

Then for more mess...
Attached part of Siglent's probes data sheet. There all these probes have same info exept BW and it is also strange. I do not anymore believe it..
What to believe now. How it can be this kind of mess.
PP215 probe pouch small info sheet: 1x: 300V&10x:600V Working voltage (Vp-p)
I have not previously looked these so carefully due to fact that no one have asked anything about over some tens of volts because it is not so common that serious users use this kind of probes for high voltage things and who ever perhaps use they are normally enough educated so that they do not need ask anything. One I have told to some people, it last normal 230Vac when 10x.
But I must say, the information is rather confusing and contradictory. I guess those who are writing these papers don't even really know what these are and how the parameters should be written so that the interpretation is unambiguous and appropriate.
So, what is final conclusion...
I can say "Who knows" until smoke come out.