The neutral wires are the return path for the electricity after it goes through the light bulbs. You should not see any voltage on them when compared to ground. Your new switches are electronic which need to be powered themselves to work so they will have their own white wire that needs to be bundled with the neutral wires.
Do you have pictures of how the old switches were wired before you removed them?
Do you have pictures of how you have the new switches wired?

Could you sketch a drawing of where you think these wires go? Does the box have a proper ground (a green or bare wire going all the way back to the breaker box)?

See below diagram and pic of wiring with old switches. I think i messed up previously as its the red traveler wire that is always hot, not the black wire (on the 3 way side). The box does have a proper ground. You can kinda see but in the back left of the box are the 4 ground wires and one is attached to the metal box.

So should I connect the red traveler wire (hot) to the load nut on the smart 3 way switch? Previously, when it didn't work, I hooked up my smart 3 way switch with the red and white wires to the traveler nuts and the black wire to the load nut and then I grounded the switch to the box and connected the neutral wire to group of three white wires. Do I just need to switch the black and red wire on the switch?

The black wire will be hot when it's energized through the 3 way switch. If you change the toggle direction at the other 3 way then the white traveler will be hot. The black wire in those pics is for the load, it won't carry any current until it's attached to the switch that you are going to install.

I believe the red and white are the travelers, meaning they take turns being hot when the other switch is changed.
Your smart switch may need to take the place of the switch that has the hot feed to it which will be a black wire, because it needs to have power all the time to work. Check the other 3 way switch to see if it has a black wire feeding it that is hot all the time.

the other 3 way switch has the hot at all times black/load wire. so how am I supposed to wire this smart switch? I created a chart of what wires are hot at what times for this switch. The N means this switch and F means the other 3 way switch.

Are you using a Kasa 3 way switch or a Kasa single pole switch?

A 3 way switch

The black at F is "line", the power comes from the breaker and is hot when the breaker is on and should be attached to the odd colored (usually black) screw on the switch.

The black at "N" is "load" and sends power to the light when it is energized from one of the travelers. Travelers can only be connected two ways and both of them are correct.

By the chart you have made I think that you are making the connections correctly, if your problem is that the light is not turning then make sure that the white from the light fixture is connected. You may have to call Kasa customer service.

I now understand the difference between load and line, thank you. Yes the "F" switch is the line and the "N" switch (the one I'm working on) is the load switch. As you are saying, this should not affect how I wire the smart switch, right? i.e. I would wire a new smart 3 way switch the same regardless of its the line or load box. Although this article seems to indicate differently (see #7 about the 'remote' switch) https://www.familyhandyman.com/project/how-to-install-a-three-way-smart-switch/

I just hooked up the other smart switch in the box, the single pole, and it works as it should. So I assume the white neutral wires are working right or the smart switch would not have worked?

About the white neutral wires. There are 3 of them, is it correct to assume that 1 goes to breaker and the other 2 go to each respective light fixture? Could it be that the white wire is connected to the light fixture on the single pole but not at the light fixture for the 3 way? Lastly, why would this matter if its the white from the 3 way smart switch is bundled with a white that is working (i.e. the single pole)?

Every light needs the white neutral wire - it's the "return" and is always unswitched. As been said above (I think), "smart" switches may also need the white wire.

It seems that travelers are discrete in smart switches, and you must account for them at both ends. This link says to order them the same way at both switches. (Step 12)

How to Physically Install the Kasa KS230 3-Way Smart Dimmer Switch | TP-Link

So i think I'm an idiot, and it originally did not work because I grounded it poorly. I wired it up again (after confirming the neutral wires work with my single pole switch) and the 3 way switch works fine. Thanks for all the help