Fix: Use a X10 scope probe that's good for your intended frequency to reduce the capacitive loading of the scope.

I built a similar "transmitters" about 55 years ago. No need for all those parts. I omitted the emitter resistor and capacitor, tying the emitter directly to the battery's negative terminal (usually used a 9 volt transistor radio battery). Omitted the resistor from the base to ground and used a 100k or 47k resistor from the base to the battery's positive terminal. A ceramic capacitor (.01 or .001 uf) across the battery terminals usually helps.

Make sure your transistor has a high enough Ft (it's in the data sheet). There are many good transistors that are not useful for RF.

With and RF choke in the collector the oscillator will oscillate at the crystal's fundamental frequency. If you replace the choke with a resonant tank you can get it to oscillate at an overtone (harmonic). We were using crystals from Citizen's Band walkie-talkies with an untuned choke for a collector load and although you could hear the transmitter's harmonics on the Citizen's Band but most of the transmitter power was around 9 MHz.

Here is a transmitter for the FM broadcast band that is nearly foolproof (no, do not add an antenna yet):
View attachment 284051
For the inductor about 8 turns of #24 wire on a pencil. Adjust the tuning range by physically distorting the coil's dimentions. You can use a 5 pf capacitor instead of the adjustable capacitor you want and only tune the transmitter by deforming the coil. Low level audio across C4 will cause frequency modulation. All of the capacitors other than C3 ceramic. The transistor can also be another small signal transistor with an Ft of 200 MHz or greater - even some 2N2222's can do that!

I will follow your diagram as soon as soon as I get the X10 probes I ordered on Amazon. I could just make a receiver with an LED to see if it works but I love seeing oscillations on scopes. Thanks a lot sir.

 

Oh, it is late and NYE. We will reconvene on the subject. 3 components and you have a scope, shouldn't be too tricky..

 

You cannot monitor RF with an LED.
Depending on the RF you can detect it on an AM MW or SW radio

 

Funny ideas some folk have. RF is energy however and if you can turn it into DC then you can turn on an LED. Better off with an old school incandescent bulb as it will light up with Anything! Happy NY, '23.