OK, so you want the lamps to be on at certain times, but dimmed.
Using old-style steam wiring, both the dimmer and the timer are devices which need power themselves. But either one would damage or cut the power the other device needs to function.
You certainly can't dim supply power to the timer, or it will be unable to do its timer thing, obviously.
Conversely, if a timer tries to turn a dimmer on and off, the dimmer will not be able to get the bulbs to "strike" at low settings. That is an artifact of how dimming works, and I'm sure you've seen this. Dimmers are designed expecting the human to go "Hey! No light!" and go to the knob and increase the dimmer light level until the bulbs strike, then back it down to the desired brightness. Well a timer can't do that, so you'll get no light at all, and leave the dimmer in a weird mode for a long time, which could damage it.
3-way wiring is certainly not constructive here, and should be avoided. 3-way human vs. timer simply makes no sense at all, and will not do anything you would want.
So let's look at options to get where I think you want to be.
Smart switches can do anything. You get a smart dimmer and a hub, and program the hub to turn the light on at X% light level at times Y:00 to Z:00 or whatever.
The important thing about smart switches is you only need 2 wires - Always-hot and neutral - to each location. Communication is done via radio (WiFi) and/or powerline signaling.
The smart dimmer could even be a smart socket or smart bulb. Anywhere you might want manual control, slap a smart switch there and tell the hub what you want smart switch activation to mean. Badabing. done.
Use just the timer, and smaller light bulbs
The easiest way to dim light bulbs permanently is use smaller or fewer bulbs.
The trick is, a 25W bulb is not as bright as a 100W bulb. However, light works on a log scale (decibels), so a 25W bulb isn't 1/4 the brightness. You may need to go dimmer, e.g. 10W or even 3W night lights. They make adapters to let you put night lights (E10 candelabra) into standard (E26 Edison) sockets.
If you want high-low light settings, consider adding some light sockets with pull cords so you can turn on the bright ones when you want them for work.
Low voltage LED lighting w/ PWM dimmer
In this case you use the timer normally. Downstream of the timer, you fit a 12v LED power supply, feeding a PWM dimmer module which has an external rheostat (knob) for control input. You need to select LED lights with resistive regulation, i.e. LED strips or puck lights. PWM dimming works a completely different way, and does not have the "strike" problem. Hence it will come on at any brightness.
Low voltage control wiring (i.e. From the dimmer module to the rheostat dimmer knob) can be done in plain thermostat wire. You would also have the design freedom to, say, fit a manual switch that selects between two fixed resistor values, giving two brightness settings. The sky's the limit on design because it's low voltage.