Probably not exactly what you're looking for
There's probably no official list of furniture prices, and pricing for individual traps. Hard to prove a negative, but there does not appear to be.
But do you really want to?
A bit of a frame challenge: how nitty-gritty do you really want to get with this?
I've been on both sides of the "building a PC stronghold", and I've yet to see it be a lot of fun to make super-detailed stronghold plans. Sure, the PCs might want to renovate the dungeon, but do you want to price it out down to every stick of furniture?
And how detailed to you want to worry about traps? The traps are a narrative detail anyway. "The next morning you find that the pit trap caught an ogre". Does it matter how much it cost to hire laborers to dig the pit?
Recommendation
Find out how enthusiastic the PCs are about this. If they're gung ho, give them broad costs for renovation depending on how fancy they want to be, somewhat similar to lifestyle costs.
If they want extra fancy things, like an observatory or something, or maybe an alchemical laboratory, price that separately.
Then get out of their way. Let them flesh it out to whatever level of detail they wish.
Be generous on mundane things. Let them stock a wine cellar or whatever.
You might be able to use official sources for some general pricing
You might be able to compare and contrast bits and pieces here and there to come up with high level prices. Depending on your economy, 100s to 1000s of gp per floor seems reasonable to me, but look at some official sources to come up with your broad estimates, see a few below.
Waterdeep: Dragon Heist provides renovation costs
Chapter 2 provides renovation costs of a $1000 gp to renovate a tavern.
The DMG provides stronghold costs
Chapter 6 of the DMG provides prices for building strongholds. You can perhaps extrapolate from that.
UA provides "bastion" pricing
Unearthed Arcana 2023, Bastions and Cantrips provides costs for adding or enlarging "basic" and "special" facilities.
Don't forget hirings
One game I was in, the DM provided us with a "major domo". This was an NPC that ran our castle for us. We paid the major domo a monthly salary. We didn't have to worry about mundane trivialities like hirelings and stocking supplies. The major domo knew how to get just about mundane thing, for a price. For instance, we wanted fancy cookies; the major domo arranged to have a bakery built within the castle and a bakery chef, specializing in cookies, hired, and gave us a ballpark cost.
We had a bunch of other hirelings, too; we never really detailed it out exactly, but we had a monthly maintenance cost. We have the major domo a lump sum that covered the monthly cost for five years and said let us know when you need more money for . . . whatever.
Get back to adventuring
Let the PCs spend however much time they want detailing their new home. They may enjoy describing it to the group. My own experience is that's moderately fun for an interlude, then players want to get back to adventuring.
The fancy cookies mentioned above were for an entity we had met in an extra-dimensional library. The entity, when asked what we could do for it, said it really had everything it needed, except the eons get lonely, and someone to occasionally have cookies and tea with would be nice. Arranging for the production of world-class cookies was interesting for about 5 minutes; having tea and cookies with an immortal extra-dimensional library entity was amusing over and over.
The mundane aspects of castle building were actually pretty boring. What we cared about was game-facing features that made us not just adventuring bad-asses, but adventuring bad-asses with a bad-ass base. Who cares how much the curtains cost.
In other words, adding a world-class bakery to our castle, about 1000 gp; hiring a bakery chef, 10 gp a month; extra-dimensional tea and cookies, priceless.