Yes and no. You were given many voices but, like most, were conditioned to use only one.
Most so-called nasal voices are actually not nasal. Nasal means much of the sound comes out the nose. More often the term gets (wrongly) used for edgy or twangy voices with predominantly mid/high mid frequency content, coming through the mouth. Well, you could argue those are "nasal" frequencies.
Without samples, it's hard to say what your voice is exactly like. But going by the examples of the other artists you provided, it's likely not nasal, just edgy.
Good mic for nasal voice
Now one can choose to record it in the most honest way (1), you could compensate (2) or you could actually highlight the edge (3). I'm no Chris Martin expert (understatement), but I've listened to some clips and there I feel there's deliberate exaggeration of the mids, plus there's heavy auto-tuning going on, which adds to that.
Should you want to go that route (3) and the mike has to be an LDC, I'd pick one with a K47 capsule. Something like an Oktavamod would be in your budget. Alternatively, you could use a moving coil (dynamic) microphone with strong mids, e.g. a Sennheiser MD421.
However, should you want to compensate (2), a mike that scoops out the mids somewhat would be the ticket. AKG LDCs come to mind.
Only very few choose to record lead vocals in the most honest way (1). That would probably be executed best by an omni SDC.
Ribbon microphones sound really smooth. That is partly caused by their treble roll-off, which does not deal with the "problem" here. But, by nature, they are also potentially less aggressive or harsh than condensers can be. So mids can actually be translated smoother, too.
Oops, you probably meant the Coldplay guy rather than Christopher Martin.
Anyway, similar story.
I had, and to an extent still have, the same problem. Bought a Blue Woodpecker ribbon, to no avail. I like it but not for vocals. With it I am losing too much of the top end. Moving the mic lower to chest level was much more helpful than buing new gear.
Just a suggestion.
Sennheiser 441 is worth considering. They can sometimes be found in the $400 range used. Not harsh, often a good vocal mic for "peaky" or edgy voices, if looking to smooth them out a bit.
Oktava 319, if you get a good one, is a very nice mic, and can be modded to sound even better. Very warm, yet with nice smooth high end detail. The sound can vary however depending on the individual mic, whereas Sennheisers are more consistent, IME.