
Samsung Galaxy Tab4 10.1
The latest firmware for Samsung Galaxy Tab4 10.1 (SM-T533) is T533XXS1BRI2 with Android 5.1.1 (Lollipop), released on September 23, 2018 for 1 region (CSC). Every official firmware build for SM-T533, newest first: one row per build with all regions (CSC) that received it.
Each firmware build has its own page at https://samfirm.shop/build/{PDA}, where {PDA} is the build number from the list above. Example: https://samfirm.shop/build/T533XXS1BRI2
SM-T533 started on Android 4 and has received 1 major Android upgrade; it now runs Android 5.1.1 (Lollipop). The newest build, T533XXS1BRI2, was released on September 23, 2018. No new build has appeared for 98 months, so regular updates for this model have most likely ended.
Box codes of SM-T533 for different colors and markets. Firmware is chosen by the model code SM-T533 and your region (CSC), not by the SKU.

SM-T537A

SM-T530X

SM-T535

SM-T532

SM-T638B
The newest firmware for SM-T533 runs Android 5.1.1 (Lollipop): build T533XXS1BRI2, released on September 23, 2018.
The latest build for SM-T533, T533XXS1BRI2, was released on September 23, 2018 (8 years ago).
SM-T533 has had no new firmware for 98 months, so regular updates have most likely ended.
Yes, all firmware files for SM-T533 are 100% official, original, and obtained directly from Samsung servers.
To flash SM-T533, you need to download the appropriate firmware, put your device into Download Mode, and use the Odin tool to load the BL, AP, CP, and CSC files.
Downgrading is only possible if the bootloader version (binary bit) of the old firmware matches the current one. Always check the binary version before flashing SM-T533.