You want to link a soundbar to a TV with a single HDMI cable, and the TV spec sheet lists only a version number, something like “HDMI 2.1 ×4”. Does that tell you whether eARC is there?
It does not. An HDMI version number is not a list of supported features.
Not because eARC has nothing to do with HDMI 2.1. The announcement the HDMI Forum issued on 28 November 2017 to release the specification puts eARC inside a list headed “HDMI Specification 2.1 Features Include”. Being in the specification and being in the product are simply two different things.
The HDMI 2.1 marketing FAQ, published by HDMI Licensing Administrator on 6 February 2022, addresses this directly. Asked whether the features are mandatory or optional, it answers: “Support for each HDMI 2.1 feature is optional.” The stated reason is that manufacturers should be able to choose what their products support based on market and price point. In exchange, a labelling duty is attached: “If the manufacturer promotes compliance with the HDMI 2.1 Specification, the manufacturer is required to list the HDMI 2.1 features supported by the product next to that messaging.”
So the place to look is not the version number but the feature list beside it. If eARC is absent from that list, the version number alone is not evidence either way.
What eARC opens up is set out in HDMI's eARC overview. It introduces eARC as an advancement over the previous ARC and states support for high-bitrate audio formats up to 192kHz, 24-bit, uncompressed 5.1 and 7.1, and 32-channel uncompressed audio. The formats it lists are DTS-HD Master Audio, DTS:X, Dolby TrueHD and Dolby Atmos. It also describes the purpose: sending audio that reaches the TV from cable, satellite, streaming or source devices onward to an AVR or soundbar over a single HDMI cable.
ARC appears in the feature list of the HDMI 1.4b specification overview. The whole description there is that it allows an HDMI-connected TV to send audio data “upstream” to an AVR or soundbar over the HDMI cable, removing the need for a separate audio cable.
There are things the documents do not answer. The eARC overview currently files the feature under HDMI 2.2, while the 2017 announcement lists it as an HDMI 2.1 feature, and neither page explains how the two labels relate. Neither states channel bandwidth figures for ARC or eARC, and neither says which codecs will pass over ARC. Which formats a particular TV sends out of its ARC port is a line to check on that manufacturer's own spec sheet.