Is strategic cyber-warfare feasible today?

The problem with such attacks is that neither the attacker nor the defender have any incentives to claim responsibility of the attack. As such attacks can be done with small number of people and the internet also makes it possible to conceal the source of an attack, a well resourced attacker can even make it impossible for the defender to realise that an attack happened at all. The defender on the other hand, would usually try its best to hide the fact that it's attacked, or to the fact that it had discovered the attack, so as not to alarm the attacker (to allow them to feed back false information), and to avoid embarrassment and erosion of public trust on the agency.

When a military cyber warfare department launched an attack against another nation's infrastructure, since there's no real witness and because most people are ignorant about how internet works and because attack forensic is hard even for experts, concealing such attacks is a lot easier than concealing physical wars. Even the defender might never realise that they are being sabotaged, or that they may have a really hard time proving that the sabotage was done by a nation state actor or figure out who the actors are, rather than, say, by a random Anonymous prankster. Additionally, the attackers themselves may sometimes not realise that they are acting under the direction of a nation state actor.

Infrastructures like nuclear power plant are more difficult to compromise purely by cyberwarfare. The reason being that there's a lot of physical safe guards (not computer controlled) and manual override systems. The most that an attacker can do is force nuclear plant worker to shutdown their sophisticated automatic control system and fallback to manually working the plant. The attack might reduce the efficiency of the power plant and increases the operational costs of the system, but it's unlikely that serious meltdown could occur from such attack.

Most attacks likely will be of the nature to increase costs of the victim, data espionage, and affect decision making. Increasing costs is fairly straight forward, with DDoS, sabotage, etc. Data espionage are more subtle but it's easily concealed by attacking random civilians, so that if the attack is discovered in government machines it'd hopefully be dismissed as random infection rather than a targeted attack. Affection decision making are even more subtle as it's essentially propaganda, targeted at specific decision maker or the entire populace for election.

Is the inclusion of a cyberwarfare branch or subcommand necessary in the sense that Cyberwarfare can affect operations and strategic outcomes

I think it's safe to say that most countries already do have Cybersecurity and Cyberwarfare capabilities.

Stock market crash

It's very difficult to say if this kind of attack are happening because stock prices are essentially decided by investors sentiments. A campaign of misinformation could potentially affect investors decision making. Spreading fake news about an upcoming political or economical instability could cause less observant investors to panic and push the market to a certain direction. This might actually trigger an actual meltdown as the initial fake wave can potentially turn into a real one.

Yes. The Russian government appears to be using attacks to destabilise the Ukraine - for some years now.

There's a well researched Wired article that has a lot of details:

https://www.wired.com/story/russian-hackers-attack-ukraine/

Then there's also NotPetya (which, you may remember, got a little out of hand):

https://www.wired.com/story/notpetya-cyberattack-ukraine-russia-code-crashed-the-world/

I cannot quantify for you, but it can certainly be said that strategic cyber-warfare is increasingly feasible - with whole swathes of vital national infrastructure now completely dependent on digital integrity. It could be argued that the feasibility of strategic cyber-warfare is increasing with exponential.

Especially so with the emergence of everyday devices which are becoming 'too smart for their own good'. They may become pawns in future warfare, especially if these devices are connected to high bandwidth. Home security is about to take on a whole new dimension.

A newish example (and possibly being forcefully deployed in an area near you) is the 'smart meter'. https://www.information-age.com/smart-metres-vulnerable-cyber-attacks-123470837/

Some intelligence agencies appear (on the surface) to be very wary of the vulnerabilities this can introduce, and rightly so.