There are two switches that are side by side. The one I'm replacing with a Smart switch does not have a neutral. The adjacent switch is a 3-way switch and it does have a neutral. Can I share the neutral from the 3-way switch for my Smart Switch? Both circuits are on the same breaker.
Looks like your switch is at the end of the line loop. That is why you have neutral and black joining in the switch. This is a case where power goes into light first, and then the switch. Possible case: https://www.buildmyowncabin.com/electrical/wiring-switch-power-into-light.html
For multiple switches, the neutrals are joined together, and that is what you see in the other 3-way using a "marrette" (I had to look this word up) https://www.buildmyowncabin.com/electrical/wiring-diagram-multiple-lights-multiple-switches.html
I think you can control by joining with the neutral from other switch (As long as you are sure that it is indeed the neutral). Put the white of current switch into your smart switch live. The black wire going into old switch into smart switch load. Neutral from other switch will go into neutral of smart switch too.
There should have been a black tape on the old switch's white wire. Not sure, it might be just the code requirement in some states (maybe also in Canada). You can add it now anyway.
These white wires aren't the neutrals you are looking for
Neither of the white wires you see in the portion of the box you have visible in your photograph is a neutral -- they're both hot or switched-hot wires that are part of a switch loop, where power and neutral come in at the light and power is continued on to the switch or switches, returning back on the other wire in the cable. This means that there is no neutral anywhere but the light box in this circuit, unfortunately, and you'll have to pull a /3 cable from one of the light boxes to the switch box to add a neutral here, replacing one of the existing /2 cables.