I've participated in a number of layoffs, and while I agree with the advice to be honest, not fake smiley, with you'll-land-on-your-feet platitudes, I would strongly recommend not talking about your own feelings. It's not about YOU (the person doing the layoff who gets to keep his job), it's about THEM (the people losing their jobs who probably earn less than you and have less financial security). Telling them how hard it is for you comes across as self absorbed and can provoke a strong negative reaction. Instead, be understanding, give them space to be angry and hurt, and help them any way you can.
I agree wholeheartedly, it's definitely not the right moment to make it about you. I have had to layoff people several times, and was laid off myself once, and the best thing to do in my opinion is to be direct succinct and stick to a script. You can still be authentic and kind, and offer them an opportunity to reach out (to you or HR) afterwards for follow up questions (about the process, not the reasons or anything sensitive). You will feel like shit doing it, and they'll be able to tell, there's no need to say it and pull the attention towards your gainfully-employed feelings at the same moment you're telling someone they're losing their financial security blanket.
I've reached out to some afterwards and offered help (serving as a reference, reviewing resumes, connecting to people, etc.) but in _that_ moment you should say as little as possible give them space to process emotions however they will.
I've had to fire people a few times. It's never fun, it's always been a hard decision that I took for the benefit of my team. It's never "bullshit". If it is bullshit then it would be MY job as manager to fix it and stop it being bullshit.
I've never had a negative reaction to the firing from the team members who remain. If anything, the reaction has always been "why did you wait so long?".
But luckily I've never had to do a team downsizing because of budget cuts. I imagine that would be a more difficult process and managing the emotions involved in that would be difficult. I see entirely why Coinbase chose not to take any of those risks and just cut everyone off first and then answer questions later.