Manu Smriti states that Earth, Water, Sky, Sun, Moon etc. are witnesses of any action that we perform.
Manu 8.86. ’The sky, the earth, the waters, (the male in) the heart,
the moon, the sun, the fire, Yama and the wind, the night, the two
twilights, and justice know the conduct of all corporeal beings.’
Now, that does not mean that Earth etc. have consciousness. It is their over-ruling deity (or the associated deity or god) that is being talked about. Like for water the god associated is Varuna. So, when it is said that "Water is the witness of all our actions" then it is to be understood that they are saying about Lord Varuna being the witness. In this manner we have to understand the passage quoted in the question too.
Because, the sense organs are also one deity (Deva) or the other. For example, Aditya (sun) is the eye, Prajapati the genitals etc.
Urdham prAnamunnayatyapAnam pratyagasyati |
visve devA upAsate || - Katha Upanishad 2.2.3
One who makes the PrANa vAyu to flow upwards and the ApAna vAyu to
flow downwards, that worship-worthy AtmA is always worshipped by the
Indriyas (senses; here senses are mentioned as DevAs or deities)
with presents (objects of the senses eventually are all for the
enjoyment of the AtmA only; this is what is meant here).
Another reference for the statement "Indriyas are actually Devas" is from Vivekachudamani:
The indriyas are the subtle counterparts of these physical organs and
form part of the subtle body. The presiding deities of these five
indriyas are, respectively, the deities of the quarters, the deity of
air, the sun, Varuna (the god of the waters) and the two Asvini
devas. (See also Panchadasi.1.19).
So, when they say "our eyes are the witnesses of all our actions" then it is to be understood that actually the deity sun (Lord Surya/Aditya) is being referred to as the witness.