If the variance of residuals is known, then can we add an extra random effect? In random-effects meta-regression, we often model an estimate of effect size ($effectSize_i$) as:
$$effectSize_i=\mu+u_i+e_i$$
where $u_i \sim N(0, \tau^2)$, and $e_i \sim N(0, v_i)$, where $\tau^2$ is the unknown between-study variance component, and the $v_i$ values are the already known sampling variances. Given, that the $v_i$ values are already known and don't need to be estimated, does that free up space for a random-effects component at the level of the effect size estimates themselves to be estimated?
Specifically, suppose the following data structure:
studyID      effectSizeiID                effectSizei       vi
1                   1                        .2           .02
1                   2                        .1           .01
2                   3                        .4           .03
3                   4                        .3           .06
3                   5                        .6           .05
.                   .                         .            .
.                   .                         .            .
.                   .                         .            .

Then, would it be theoretically possible to fit (note the use of additional grouping variable effectSizeiID) the following?
library(metafor)

## DON'T RUN:
rma.mv(effectSizei ~ 1, vi, random = ~ 1 | studyID / effectSizeiID, data = data)

The above model (if treated as an ordinary random-effects model) will NOT be identifiable:
library(nlme)

## DON'T RUN:
lme(effectSizei ~ 1, random = ~ 1 | studyID / effectSizeiID, data = data)

 A: Yes, by fixing the sampling variances to their (approximately) known values, we can examine if the observed effect size estimates vary as much as would be expected given these variances or if there is more variability. If they vary more, then this suggests that the underlying true effects are 'heterogeneous' (i.e., they also vary). Under the random-effects model, we can in fact estimate the amount of variance in the underlying true effects (i.e., $\tau^2$).
In a model where you add random effects at the level of some higher grouping structure (e.g., studyID in your example), you should add these random effects to the model, not use them to replace the random effects at the level of the estimates. Otherwise, you would be assuming that the true effects are homogeneous within each study, a tenuous assumption in many situations. Hence, you really should use random = ~ 1 | studyID / effectSizeiID and not just random = ~ 1 | studyID. This is also discussed here: https://www.metafor-project.org/doku.php/analyses:konstantopoulos2011 (see the section titled "A Common Mistake in the Three-Level Model").
A 'regular' random/mixed-effects model (with raw data and assuming normally distributed errors) is different in that we do not fix the error variance to some known value and instead estimate it from the data when fitting the model, usually assuming that the error variance is the same for all rows in the dataset, but one can relax this assumption and also allow $\sigma^2$ to differ for example for different groups.
