Products of electrolysis of Ni(NO3)2
Some electrolysis experimets are best first performed and then an attempt  at explanation.
For example, the products of the electrolysis of aqueous nickel nitrate with graphite electrodes are reportedly per a source (with video) as:

Electrolysis of a nickel nitrate solution produces oxygen at the anode, and hydrogen and nickel at the cathode.

Looking at related metal electrolysis, for example, Cu(NO3)2, per this source with again graphite electrodes:

Electrolysis of a copper(II) nitrate solution produces oxygen at the anode and copper at the cathode.

Lastly, with the transition metal manganese, a source on the electrolysis of Mn(NO3)2, reports, to quote:

$\ce{Mn(NO3)2 + 2H2O ± 2e- -&gt; H2 + MnO2 + 2HNO3}$

Based on all of the above, and that hydrogen gas is forming per the reactions:
$\ce{H+ + e- -&gt; .H }$
$\ce{.H + .H  -&gt; H2 (g)}$
I would expect similarly some transient nitric acid formation with Ni(NO3)2 per its potential interaction between the nitrate ion and the hydrogen atom radical as follows:
$\ce{ NO3-  + .H  -&gt; .NO2  + OH-}$
$\ce{.NO2 + .NO2 &lt;=&gt; N2O4 }$
$\ce{N2O4 + H2O -&gt; HNO2 + HNO3 }$
Note, my claimed introduction of HNO3 (and its likely subsequent removal by nickel metal) can explain the comment &quot;the molarity of the solution remains constant as nickel's active, and dissolves and deposits in equal measure&quot;, and is also consistent with the electrolysis of Mn(NO3)2 resulting in the creation of nitric acid.
And lastly, you are correct, oxygen is produced at the anode.