Jump vs Warp to X in cloaky ships

I'm a new player in Eve Online who generally is flying Covert Ops ships in nullsec for relic/data sites. Since I need to return to hisec regularly to sell my goods, I find myself constantly passing through camped stargates.

My question is about the safety of the 'Jump' option. Most of the forums posts I've seen regarding safe jumping typically reference "Warp to zero, then spam jump", which seems obsolete now with the "Jump" option (mentioned posts from 2012-ish).

Incidentally, many forum posts also advise for cloaky ships to "Warp to X" (where X is greater than 0) to avoid the 2km de-cloak and to slowboat--undetected--till 2500m where I can initiate Jump without being decloaked by the gate itself.

I'm looking for a more modern answer to the question: can a cloaky ship safely use "Jump" to leave a system?

I feel like I am constantly left waiting adjacent to the departing gate--decloaked and vulnerable--but I've never been locked (or even attempted). Is this lucky or a by-product from already having initiating the new session?

The point where you're vulnerable at a gate is after you jump through, before you jump you're safe. The time you need aligning and/or the time needed to fly out of a bubble is the dangerous part.

When warping to a gate, during your warp you are invulnerable, and after activation of the jump sequence you're invulnerable as well. There is simply not enough time between the end of your invulnerability in warp and the start of the jump for an enemy to lock you.

The somewhat newer Jump command is generally safe, and pretty much identical to manually warping and then pressing jump. The "spamming" advice is mostly because you want to jump directly after your warp ends, and it is easier to spam the button than to determine if you're actually out of warp, and because under bad conditions commands can be lost.

There are situations under which you're not safe landing on the gate, sometimes your jump command will be denied. There are two big reasons for this, the first one is "traffic control". Sometimes you get a message like "You've been cleared to jump within xxx seconds" and your jump command is ignored. This has technical reasons, you get this message e.g. if you play directly after the downtime and nobody has entered that system yet. The really important part is that your jump command is cancelled when you see that message, and that the message is misleading and the time mentioned does not indicate anything useful. You might be able to jump a few seconds later, or not. Don't bother petitioning losses that result from such issues, I tried and it doesn't work.

The other important case that prevents you from jumping is if a system is too full, Jita often hits the population cap and you'll be blocked from entering. Spamming jump often works quickly then, as people constantly leave the system as well, but you might be exposed for quite some time on the gate if you're unlucky.

Under good conditions a single Jump command to the gate is perfectly safe, but if there are any network issues or server issues, this might not be the case. So you should always keep an eye on whether you actually jumped or got an error message.