Define your real objectives in specs 1st; Frequency tolerance, Rise/fall time limits, output impedance or load impedance, capacitance. THIS PROCESS OF LISTING DESIGN SPECS IS MANDATORY FOR ALL GREAT DESIGNS. (Even if you change them after testing to correct poor assumptions) Then you can choose the best topology.
The flaws in this design are obvious to any senior designer and are well listed in comments and other answers. But the real goal is how to make it better by good specs, then better choices. However, I will show how to stabilize this primitive design and protect Veb and Pd max of each part.
It can be made safe using a reverse diodes or reversed current limited LEDs across Vbe , but then it ramps up faster with a small ramp voltage from -0.7 to 0.6V so Rb may need to be reduced < 50% and C must be increased 20x to get full voltage.
Without the added Rcl, current limit the Transistor acts as a 1 ohm switch with 26 V charged on large caps , displacing large current negative spikes quickly but safely > -6V if rated large enough.
Rb/Rc must be greater than hfE to get full swing to a non saturated Vce around 1 to 2 V and C must be increased to lower f.
Then the 1k resistors must be made from 4 x 1k 1/4W Rs in 2S2P to dissipate and share ~ 670 mW.
For even a better solution using BJT's only, use White , Blue or Green LEDs and current limit with Rcl= 680 ohms on the collectors to just above 30 mA with same 1k pullup Rpu, for the pulse current to be safe and also more stable. and reduce the 1k power dissipation to 250 mW 50% d.c. at 85'C . (hot)
Proof of concept
The power diode version runs faster as explained.
The multi-vibrator works well with Vcc=5V providing a -5V base Sawtooth to ramp up to Vbe= 0.6V then switch again. But higher Vcc's demand a clamped negative Vbe voltage such as a 3V LED or 4.7V zener. (reversed to clamp negative voltages). or even a two 2V LED's in series. They won't illuminate as the current limit Rc and low duty cycle only clamp for a very low duty cycle then the RC ramp to Vbe controls the cycle time. People get away with higher 9V Vcc's because the average power in Veb reverse current dump is < 150 mW, so it appears to survive but can wound the junction to fail sooner than expected.