I have only transited through T3 on ITI connections so I cannot answer your question with any kind of authority.
sleepinginairports.net has this to say:
Rest & Relaxation Zones
Several rest areas have been set up for travellers to relax between
flights.
Terminal 2
Window Lounge – Relax among the china doll trees in one of six comfy lounge chairs as you watch planes take off and land
through a panoramic 10-meter window. This cozy, carpeted area is in
T2, airside, between Gates 36 – 39.
[...]
Oasis Lounge – Mobile
charging, comfy couches, and TVs are available in this carpeted,
green-toned waiting lounge. Location: T2, airside, Transfer Hall on
F1.
[...]
Hotels inside Beijing Airport
Hourly Hotel – Inside the terminal are “hourly lounges,” which feature standard rooms with bathrooms. Locations: [...] Terminal 2, International Arrivals, B1, middle of D2 and D3 [...] According to a reviewer in July 2017, the rates were RMB 500 (Terminal 2, 4-6 hours for a single standard with bathroom) • 380RMB (Terminal 2, 4-5 hours for a single standard without bathroom) [...] Showers are 50RMB per person.
GoSleep Pods – The sleeping chair/pod has a cover to block light/noise and storage under the seat to secure personal items. Electronic devices can be recharged inside the unit. Pods can be used for 1 hour or longer. Location: Terminal 2, Airside, near Gate 38
Gate 38 is airside in the international part of the terminal. Please be aware that much of this information might be outdated. Kindly update it (especially sleepinginairports.net) if you have more recent information.