Hint it and measure enthousiasm
The general approach I take when I'm not sure what my players like, or whether they'd enjoy a specific thing, is to hint to it during the session and see if they bite. This works best in an open world or if you've already taught your players that they can say "no" and the story will go on, but even if they're used to being railroaded around you can still drop hints to events and see if they bite.
The basic idea is to include the direction you'd want to take in something that is obviously not directly related to what the players are doing. Commonly used for these purposes are rumours, idle chatters, news reels playing in the background, headlines in the paper, etc.
Think of how in movies there is often a movie-set on while the main character is leaving to go somewhere and then just after he slams the door, the camera lingers for a bit and lets you hear the last part of a crazy news report about "possible aliens spotted" or "scientist does crazy invention; is world doomed?" or what have you.
You can have those in your game, too. The next time the players are in a bar, describe how the radio is on and they overhear how a missing kitten was found, a 100-year old man was visited by the mayor, and a resident crazy person claims their best friend was eaten by a dusty book they found in the attic. See whether the players remark on the last story and whether they think it's interesting. (This can be in character or out; either means it has peaked their interest)
If you get an initial reaction, bring that story, or elements of it, back later. Keep them in the background, but let the players get a glimpse of how it's going. Make it sound like whoever is dealing with it, could use a hand. But don't make it sound like they ought to get involved yet. Again, measure their reaction to it. If they have at least something of a reaction, you can drop the story more directly into the game. Have them meet someone who is part of the investigation, who tries to contact them for help. Preferably while they are in the middle of something. Let the tone simmer through in the way this request is formed; this'll be the first time that you really present the tone you're aiming for, but while the players are busy.
If they immediately drop everything to help this person; they are really interested in changing tone. Go wild. If the players sound enthousiastic, but the characters want to finish their current job first, they are also interested in the new tone, but make the change more slowly, so they can get used to it. If the players sound confused or seem to accept more out of an "oh, this will be the next story" line of thought, they are probably not very interested and I would consider running the core of the story in your original tone, or just dropping it altogether. These players might enjoy the tone, but not in the current game.
If they flat-out refuse to help or protest out of character, they probably don't want to run in the given tone at all and you should probably drop it and maybe apologise for bringing it up.
I feel this is also important to mention. While the above makes it possible to change the tone of a campaign slowly, I would not actually advise doing it. (It's more suited to introducing new topics and stories).
The reason here is that (most) players design their characters and background and set their expectations based on the originally described tone of the game. Characters grow in the direction of the original tone, too. But your new tone would probably be better suited with completely different kinds of characters.
For example, if I know there's going to be a lighthearted cyberpunk game, I might run a glitching cyborg, a tough jock who's afraid of talking to robots, or a street-rat who mugs rich people with a robotic monkey-sidekick. Light-hearted, fun characters to play.
But if you suddenly start changing the tone to something creepy and horrific, these characters would probably not be appropriate.
If you wanted to run a cyberpunk chtulhu game, I'd much rather have heard beforehand, so that I could have created a android infected with a virus that interferes with his motor controls and occasionally his judgement, an ex-army guy who has severe paranoia after nearly being killed by a friendly drone-trooper over a joke, or an orphan who has been without a community so long, he thinks his mindless automaton is actually his friend.
Characters suitable for such kind of game, for whom I'd have explored the background that lead them to where they are and whose mannerisms are designed around a serious theme and for whom I've thought about the horrible fate probably awaiting them.
(Note that the first and second examples are intentionally the same characters, just described for a different kind of tone of campaign. The tone matters hugely in how people portray characters, which parts of their background they write out and what goals they set for them. I wouldn't enjoy losing that work and having nothing to fall back on because the tone switched without my knowing.)