......dropping down from the top of the tube Fender style or laid flat to the chassis ...
Well, it depends... How good are you at thinking in 3-D?
Fender did it at least 2 ways.
Original tweed amps lay the heater wires against the chassis, but dressed away from the sockets and tucked into the lip formed at the chassis edge, as shown below.

Next image is an actual vintage Fender tweed amp, but someone re-did the heater wires (probably because the amp was old enough to ground 1 heater pin at all 6.3v tubes to use the chassis in place of one of the heater wires). Notice this puts the heater wiring
closer to the board components, and also makes the working area more cluttered. Fender didn't do it that way, in these amps.

So the "Fender rule" is if the sockets are at 90-degrees to the board/components, dress the heaters against the chassis to keep them away from the board.
The photo below shows a 60's-era Deluxe Reverb. Now the sockets are on the same plane as the board, and the heaters are dressed up in the air and drop down to the sockets. That keeps them at max distance away from everything.

Not everyone followed these "rules" or even considered twisted heater wiring mandatory. McIntosh made many hi-fi items and typically rotated tube sockets so heater pins of each were aligned, then passed a bare solid wire straight through similar-pins of each socket. So that places 1 side of the heater wiring on either side of the socket. See below.

Soldano did the same, as well as making other common connections between output tube sockets in this buss-fashion.

I did a variation of some of these in an amp I built by passing my heaters flat along the chassis, but running wires from socket-to-socket directly on top of the socket instead of going in the air or around. When I generated my layout, I knew I'd have the components mounted between parallel strips with the tube sockets themselves below the components (the way Tektronix built their tube scopes). Running the heaters right-to-left against the chassis kep that wiring at 90-degrees to the socket pins themselves (on one plane) while also keeping it at 90-degrees to the components (on another plane). It seemed to me the neatest way to wire them while minimizing the chance of hum would be this unconventional arrangement. I've had zero hum issues.

So it just depends on your circumstances and what your experience tells you should work best (or well-enough). If you don't have the experience to draw from, copy what worked for others, as long as your situation also truly matches what their situation was.