As others have said, you'll have about as much luck, and at least as much of a job, as trying to get ST Mono to display on a normal TV. The signals produced by the XE are fundamentally incompatible with what the SM range expect in almost every way - Horizontal frequency (35.8kHz vs 15.7kHz), vertical frequency (71.5Hz vs 50.0 or 59.9Hz) and line count (~501 progressive vs ~312 or ~262 progressive/~625 or ~525 interlaced), TTL (allegedly) pixel intensity instead of analogue, separate syncs instead of a composite signal (which is the case even with S-video), probably even things like sync polarity, active/visible proportion of the scanline/frame, etc.
You'd probably be better off trying to transplant the innards of a regular TV or (monochrome?) 15kHz composite monitor with the same size tube into the body of a dead SM or SC; the look would be almost completely unaffected, and you'd be able to plug the XE straight in and get a pure, authentic image out of it without any messing about with or image degradation caused by running the signal through a scaler. Plus you'd be in a position to adjust the raster size and position so it was nicely centred and just nudging the corners of the bezel (not at all guaranteed otherwise), and above all you'd be saving at least the shell of a classic monitor that would otherwise have been destined for the scrapheap.
Alternatively if you can get hold of an SC, I've seen a diagram recently for connecting an ST (in low/med rez, ie the colour modes) to a monochrome 15kHz composite monitor, which essentially meant bridging all three colour lines (optionally through resistors to cap the total voltage and bias the appearance for the normal condition of green being the "brightest" primary and blue being the "darkest") plus the Csync line (or H and V sync through a combiner for machines that lack it) onto the live pin of a composite cable, and the various grounds to the shield.
You could probably, therefore, attempt the reverse; get a simple sync splitter chip, run the composite or luma (from SVideo) signal into that, then squirt the H/V syncs so produced onto the appropriate lines in the cable, and bridge the stripped composite or luma signal across all three of the colour lines unaltered (or just green if you want to run greenscreen, or with appropriate resistors onto red and green for amber). In both cases there might be a need for an inverter somewhere along the line otherwise the image might turn out negative (and the syncs might also be incorrect polarity), but that's not a particularly big ask. Other than for the fact that it runs negative intensity (IE zero volts is maximum brightness, and higher voltages make darker pixels), a monochrome composite video signal (ie colourburst disabled, or using only the luma of an S-video) is a pretty simple thing... over the active areas the voltage corresponds directly to the beam intensity as it sweeps across the raster, and the syncs are overlaid onto it (using "blacker than black" voltages) in the blanking areas. So there's no particular magic in converting it to/from a bridged-RGB pseudomonochrome image.
You wouldn't get the completely smooth look of a true monochrome screen, that way, but it would certainly look sharp enough to fool the casual observer; the XE's maximum spatial resolution is a little less than that of the ST in low rez mode, and the SC had a fine enough dot pitch to make extended sessions in medium rez (ie 80 columns) perfectly comfortable. The phosphor is probably a little longer persistence than that of the SM, too, meaning 60Hz (which you may as well run even if your machine is PAL, because of the 192-line limit) shouldn't seem that much more flickery than 71Hz, and it will certainly be less flickery than an SM coerced into running at 60Hz...
If you're dead set on using the SM, you'll have to start with a decent scan converter/upscaler that can produce a genuine ~72Hz (not merely "70Hz"), ~36kHz (not "31kHz", not "31.5kHz", and probably not "37kHz") VGA-esque signal from a composite input, preferably with full control over the scan characteristics. The SM's horizontal scanning frequency is akin to the original SVGA and XGA standards, but the line count is lower than almost any VGA standard other than the early 350- and 400-line EGA/CGA compatibility modes and some of the more exotic flavours of 72~85Hz not-quite-VESA enhanced refresh rate, and it's not quite 72Hz itself either. It might be able to adapt to a reasonably close preset, but if you can set the output frequency yourself that'd be better (pixel clock somewhere in the 25 to 32MHz range with around 80% of the total active including the XE's borders (you can expect maybe 72~75% to be visible as a minimum), ~35.8kHz, ~71.5Hz, about 501 lines). After that you'll at least need to bridge the RGB down to monochrome (or if you have absolutely mono input, you could just use e.g. the Green line), preferably with the resistors to tune the colour to a TV-like appearance (IE different hues of the same luminance produce different intensities on-screen), if not in fact convert the output to TTL levels. In the latter case, you'll only be able to get pure black-or-white output on the screen, but if it accepts analogue intensity you'll have greyscales.
I mean, it's not outside the realm of possibility, but you might find it an expensive, frustrating exercise with a disappointing output quality. And after all that you'll likely still want to adjust the SM itself to expand the image a bit, especially in the vertical dimension (and perform some prophylactic modifications to prevent some of the more marginally specified parts, particularly some notoriously fragile power filtering capacitors, from dying in short order when pushed beyond their design specs), which is something best left to a CRT service engineer if you're not experienced with them. (Though a suitably flexible scaler might allow you to line-triple instead of line-double, and expand the XE's 192 active lines to 432 on the SM instead of what would be a quite markedly letterboxed 384...)