That is definitely not a 63cm. Maybe 60cm tops. How are you measuring ? Different manufacturers measure differently but the correct universal measurement of a frame is always center point to center point, not center of bottom bracket to top of seat tube.

Measure your frame from these 4 points.
(1) Center of Bottom Bracket to Center of Seat Tube / top tube intersection. This is your actual frame size.
(2) Center of Head Tube horizontally to Center of Seat Tube ( horizontal measurement of the top tube )

As some of us suspect that frame is a 58-60cm, that top tube should be about 57.0 to 58.0, more likely a 57.5cm

My question though is why would you buy this bike considering you are having neck issues, that stem at 130mm was correctly setting up the previous owner to ride in the drops and on the hoods with a flat back. By reducing to a 60mm you have drastically changed the handling characteristics of the bike, ( twitchy ).
You sound ( from your description ) that you would be better off on a straight bar setup. I you never use the 3 positions of drop bars then it's pointless to be on that bike. Looking at the pic you are trying to fit yourself to the bike, actually it should be the other way around. Fit the bike to you, 1st taking into account your physical limitations.

Also correct fit of a bike is not determined by standing on the ground straddling the top tube. If that were the case then no one would fit a Penny Farthing.
Fit is determined by (1) Leg inseam (2) Arm reach as measured from palm to armpit but shoulder is really more accurate. (3) Shoulder width to be matched with handlebar widths. (4) Torso, hip bone to just under your arms. Wether in the drops ( inconsequential here ) or on the hoods or bar tops, critical is being able to breathe without constriction. If you are scrunched up because the bars are too narrow or/and you are not able to stretch your back out ( see old pics of riders with very rounded backs, like a turtle. most recent to mind would be Andrei Tchmil )
Once you have your body's measurements then you spec out a correct frame size and then dial in stem length, seat height, seat setback, crank lengths, handlebar widths etc..

The reason to measure a bike along these parameters is to be in control when riding. You want to be centered on the bike, not with your weight center of gravity too far forward or too far aft or too far vertically.

This is my old bike soon to be retired ( frame ). it is a 60cm really more a 58cm but as I said earlier, Trek measures differently than Cannondale. Anyway TT on this is a 57.5 and seat tube is a 56 cm. If you look at the head tube and compare it to your bike they are very close, so " NO " the bike you bought is definitely not a 63cm



However, since that is a carbon fork tube, it seems that it is stacked way too high.