We present a compact diode side-pumped continuous-wave (CW) Tm,Ho:YAG laser oscillator with high brightness at 2.09μm. After carefully optimizing the system elements, this laser delivers a maximum output power of 21.9 W with an optical-to-optical efficiency of 6% at a temperature of 12°C. The average beam quality is measured to be M2=3.17, leading to a brightness value of up to 50 MW/cm2⋅sr. To the best of our knowledge, this represents the highest brightness for any Tm,Ho co-doped laser oscillators operating at near-room temperature (NRT).