The current redshift record is set by the JADES galaxies. The highest-redshift one at $z = 13.20$ isn't too convincing tbh, but there's one at 12.6 that looks better, and the one at $z = 11.6$ should be good enough. But if we go with z ~ 13, then according to the answer you link to, the volume of the "observed" Universe is $\simeq150\,000\,\mathrm{Glyr}^3$.
In that answer, I equated that to 10% more than in the pre-JWST era. However, this was based on the prior redshift record of GN-z11, which had been measured to $z\simeq11.1$ (Oesch et al. 2016). But that redshift was, as is the case with the JADES galaxies, measured in a somewhat imprecise way, namely by the spectral break at the Lyman α line. That is, there wasn't any spectral lines, but just the break that comes from the intergalactic medium absorbing any radiation bluer than Lyman α, and the exact wavelength of this break depends on many obscure factors.
With JWST, it is now possible to observe such lines from GN-z11, and its redshift has been established at $z=10.60$ (Bunker et al. 2023). This actually means that the observed Universe was a little smaller before than we thought. It seems a little like cheating, but this in turn means than the fractional increase is a little larger, so 13% instead of 10%.
Gravitational lensing does indeed help observing more distant galaxies, and for this reason JWST has targeted several massive galaxy clusters, to look for distant background galaxies. These galaxies were unlensed though.
The plot below shows the probed volume as a function of the redshift of the most distant known galaxy. Since the very first galaxies are thought to form at $z\simeq20\text{–}30$, an increase of more than $\sim50\%$ is unlikely. But stay tuned; I'll update this plot along the way :)
![enter image description here](https://cdn.statically.io/img/i.sstatic.net/FCelt.png)