Take a look at the FeinTech VAX01202. It's available at amazon.

FeinTech offers 2 adapters, please do not mix them up:
Old TV & new soundbar > VAX04101A
New TV & old AV receiver > VAX01202

So with the VAX04101A it is possible to run Sonos Arc in Atmos with old TV or video projector if the Shield is connected .

the TV must have ARC if it has 4k. it can't be that old. maybe ARC isn't written on it. And the cable must be ARC-capable.
Doesn't the soundbar have an optical input?
PS: The soundbar alone does not bring ATMOS ;) Then I would buy a proper Yamaha 7.1 or 9.2 amplifier in your place and enjoy ATMOS.

PS: FeinTech writes in the Q&A on Amazon that you need the VAX04101 for an Arc or eArc connection and that this also works with Sonos.

Thank you @jfrompf87 for the impetus. 👌

Thank you, looked good until:
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The VAX01202 can NOT be operated on an HDMI-ARC or HDMI-eARC connection of a soundbar. Only on a normal HDMI input of an AV receiver, for example "AUX" or "Bluray". If the soundbar has only a single HDMI connection, it is almost certainly an HDMI-ARC connection, which will NOT work with the VAX01202. The VAX01202 will not work with any Sonos sound system.
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Unfortunately, I have the Arc. I probably won't be able to avoid replacing the TV. But I'm not doing it just because of Atmos.