$c =$ $\frac{m}{s} =$ the speed of light.
$G =$ $\frac{m^3}{kg \cdot s^2} =$ gravitational constant
$k_e =$ $\cdot \frac{kg \cdot m^3}{C^2 \cdot s^2} =$ {{Coulomb_constant_in_kg_m3_per_C2_s2}} $\frac{kg}{C} \cdot \frac{m^3}{C \cdot s^2} =$ Coulomb's constant.
(Coulomb's constant units are the same as the gravitational constant's units, but with $kg$ swapped with $C$, and then with an extra ratio of $kg$ to $C$.)

Derived values:
$\epsilon_0 = \frac{1}{4 \pi k_e} =$ {{vacuum_permittivity_in_C2_s2_per_kg_m3 = 1 / (4 * Math.PI * Coulomb_constant_in_kg_m3_per_C2_s2) }} $ \frac{C^2 \cdot s^2}{kg \cdot m^3} =$ {{vacuum_permittivity_in_C2_s2_per_kg_m3}} $\frac{C}{kg} \cdot \frac{C \cdot s^2}{m^3} =$ vacuum permittivity.
$\mu_0 = \frac{1}{\epsilon_0 c^2} =$ {{vacuum_permeability_in_kg_m_per_C2 = 1 / (speed_of_light_in_m_per_s * speed_of_light_in_m_per_s * vacuum_permittivity_in_C2_s2_per_kg_m3)}} $\frac{kg \cdot m}{C^2} =$ {{vacuum_permeability_in_kg_m_per_C2 }} $\frac{kg}{C} \cdot \frac{m}{C} =$ vacuum permeability.

To boot, how about those gravitomagnetic permittivity and permeability:
$\epsilon_G = \frac{1}{4 \pi G} =$ {{gravitomagnetic_vacuum_permittivity_in_kg_s2_per_m3 = 1 / (4 * Math.PI * gravitational_constant_in_m3_per_kg_s2) }} $ \frac{kg \cdot s^2}{m^3}$ = gravitational vacuum permittivity.
$\mu_G = \frac{1}{\epsilon_G c^2} =$ {{gravitomagnetic_vacuum_permeability_in_m_per_kg = 1 / (speed_of_light_in_m_per_s * speed_of_light_in_m_per_s * gravitomagnetic_vacuum_permittivity_in_kg_s2_per_m3)}} $\frac{m}{kg} =$ gravitational vacuum permeability.

In both cases, $\frac{1}{c^2} = \mu_0 \epsilon_0 = \mu_g \epsilon_G = $ {{1 / (speed_of_light_in_m_per_s * speed_of_light_in_m_per_s)}} $\frac{s^2}{m^2}$.

natural units, setting $c = G = k_e = 1$
$1 = \sqrt{k_e \cdot G} =$ {{sqrt_ke_G_in_m3_per_C_s2 = Math.sqrt(Coulomb_constant_in_kg_m3_per_C2_s2 * gravitational_constant_in_m3_per_kg_s2)}} $\cdot \frac{m^3}{C \cdot s^2}$
$1 = \sqrt{\frac{k_e \cdot G}{c^4}} =$ {{C_in_m = sqrt_ke_G_in_m3_per_C_s2 / (speed_of_light_in_m_per_s * speed_of_light_in_m_per_s)}} $\cdot \frac{m}{C}$, so $1 C =$ {{C_in_m}} $m$.
$1 = \sqrt{\frac{k_e}{G}} =$ {{C_in_kg = Math.sqrt(Coulomb_constant_in_kg_m3_per_C2_s2 / gravitational_constant_in_m3_per_kg_s2)}} $\cdot \frac{kg}{C}$, so $1 C =$ {{C_in_kg}} $kg$, and $1 kg =$ {{kg_in_C = 1 / C_in_kg}} $C$.
Therefore, using natural units, $k_e =$ {{Coulomb_constant_in_m3_per_C_s2 = Coulomb_constant_in_kg_m3_per_C2_s2 * kg_in_C}} $\frac{m^3}{C \cdot s^2} =$ {{Coulomb_constant_in_m3_per_C_s2 * kg_in_C}} $\frac{m^3}{kg \cdot s^2}$ by unit conversion.
(Which makes sense if $k_e = G = 1$, then of course their conversion to identical units will have an identical value).

equilibrium fluid:
TODO the derivation
$T_{ab} = (c^2 \rho + P) u_a u_b + P g_{ab}$
$\left[ T_{ab} \right] = \frac{kg}{m \cdot s^2}$
for:
$\rho = \left[ \frac{kg}{m^3} \right] =$ density
$P = \left[ \frac{kg}{m \cdot s^2} \right] =$ pressure
$u_a = \left[ 1 \right] =$ 4-velocity.

electromagnetic field:
$T_{ab} = \frac{1}{\mu_0} (F_{au} F_{bv} g^{uv} - \frac{1}{4} g_{ab} F_{uv} F^{uv})$
$\left[ T_{ab} \right] = \frac{kg}{m \cdot s^2}$
for:
Faraday tensor:
$F_{ab} = \frac{1}{c} 2 E_{[a} t_{b]} + \epsilon_{abcd} t^c B^d$
$\left[ F_{ab} \right] = \frac{kg}{C \cdot s}$
$t_a = \left[ 1 \right] =$ timelike unit vector, such that $t^a t_a = -1$
$E_a = \left[ \frac{kg \cdot m}{C \cdot s^2} \right] =$ spatial electric field, such that $t^a E_a = 0$
$B_a = \left[ \frac{kg}{C \cdot s} \right] =$ spatial magnetic field, such that $t^a B_a = 0$

Substituting:
$T_{ab} = \frac{1}{\mu_0} ( (\frac{1}{c} 2 E_{[a} t_{u]} + \epsilon_{aucd} t^c B^d) (\frac{1}{c} 2 E_{[b} t_{v]} + \epsilon_{bvef} t^e B^f) g^{uv} - \frac{1}{4} g_{ab} (\frac{1}{c} 2 E_{[u} t_{v]} + \epsilon_{uvcd} t^c B^d) (\frac{1}{c} 2 E^{[u} t^{v]} + \epsilon^{uvef} t_e B_f) )$
$T_{ab} = \frac{1}{\mu_0} ( 4 \frac{1}{c^2} E_{[a} t_{u]} E_{[b} t_{v]} g^{uv} + 2 \frac{1}{c} E_{[a} t_{u]} \epsilon_{bvef} t^e B^f g^{uv} + 2 \frac{1}{c} \epsilon_{aucd} t^c B^d E_{[b} t_{v]} g^{uv} + \epsilon_{aucd} t^c B^d \epsilon_{bvef} t^e B^f g^{uv} - \frac{1}{c^2} g_{ab} E^{[u} t^{v]} E_{[u} t_{v]} - \frac{1}{2} \frac{1}{c} g_{ab} E^{[u} t^{v]} \epsilon_{uvcd} t^c B^d - \frac{1}{2} \frac{1}{c} g_{ab} \epsilon^{uvef} t_e B_f E_{[u} t_{v]} - \frac{1}{4} g_{ab} \epsilon^{uvef} t_e B_f \epsilon_{uvcd} t^c B^d )$
$T_{ab} = \frac{1}{\mu_0} ( \frac{1}{c^2} E_a t_u E_b t_v g^{uv} - \frac{1}{c^2} E_u t_a E_b t_v g^{uv} - \frac{1}{c^2} E_a t_u E_v t_b g^{uv} + \frac{1}{c^2} E_u t_a E_v t_b g^{uv} + \frac{1}{c} E_a t_u \epsilon_{bvef} t^e B^f g^{uv} - \frac{1}{c} E_u t_a \epsilon_{bvef} t^e B^f g^{uv} + \frac{1}{c} \epsilon_{aucd} t^c B^d E_b t_v g^{uv} - \frac{1}{c} \epsilon_{aucd} t^c B^d E_v t_b g^{uv} + \epsilon_{aucd} t^c B^d \epsilon_{bvef} t^e B^f g^{uv} - \frac{1}{4} \frac{1}{c^2} g_{ab} E^u t^v E_u t_v + \frac{1}{4} \frac{1}{c^2} g_{ab} E^v t^u E_u t_v + \frac{1}{4} \frac{1}{c^2} g_{ab} E^u t^v E_v t_u - \frac{1}{4} \frac{1}{c^2} g_{ab} E^v t^u E_v t_u - \frac{1}{4} \frac{1}{c} g_{ab} E^u t^v \epsilon_{uvcd} t^c B^d + \frac{1}{4} \frac{1}{c} g_{ab} E^v t^u \epsilon_{uvcd} t^c B^d - \frac{1}{4} \frac{1}{c} g_{ab} \epsilon^{uvef} t_e B_f E_u t_v + \frac{1}{4} \frac{1}{c} g_{ab} \epsilon^{uvef} t_e B_f E_v t_u - \frac{1}{4} g_{ab} \epsilon^{uvef} t_e B_f \epsilon_{uvcd} t^c B^d )$
$T_{ab} = \frac{1}{\mu_0} ( t_a t_b ( \frac{1}{c^2} E_u E^u + B_u B^u ) + \frac{1}{c} (t_a \epsilon_{bcde} + t_b \epsilon_{acde}) t^c E^d B^e - \frac{1}{c^2} E_a E_b - B_a B_b + \frac{1}{2} g_{ab} ( \frac{1}{c^2} E_u E^u + B_u B^u ) )$

What about, alternatively, an equilibrium fluid but with electromagnetic terms instead?
$T_{ab} = \sqrt{\frac{k_e}{G}} ( (c^2 \rho_{charge} + \phi) u_a u_b + g_{ab} \phi)$
$\rho_{charge} = \left[ \frac{C}{m^3} \right] =$ charge density.
$c^2 \rho_{charge} = \left[ \frac{C}{m \cdot s^2} \right]$
$\phi = \left[ \frac{C}{m \cdot s^2} \right]$ is the electrical equivalent of pressure.
$J_u = (c \rho, j^i)$ in units of $\left[ \frac{C}{m^2 \cdot s} \right] =$ current density.
$u_a = \frac{1}{c \cdot \rho_{charge}} J_a$ is in units $\left[ 1 \right]$