Let $X$ and $Y$ be smooth complex varieties and $M\in D^b_{\mathrm{hol}}(\mathscr{D}_X)$ resp. $N\in D^b_{\mathrm{hol}}(\mathscr{D}_Y)$ holonomic $\mathscr{D}$-modules (resp. complexes with holonomic cohomologies). Furthermore let $(\bullet)^{\mathrm{an}}$ denote the analytification functor from GAGA. For the regular holonomic case, it is true that $$(M\overset{D}{\boxtimes}N)^{\mathrm{an}}\simeq M^{\mathrm{an}}\overset{D}{\boxtimes}N^{\mathrm{an}}$$ (where $\overset{D}{\boxtimes}$ is the external tensor product of $\mathscr{D}$-modules). What I would really like to know is:
Is this true in the non-regular setting as well? If not, does it hold under any further assumptions on $M$ and $N$ (i.e. meromorphic connections etc.).
Any references, thoughts and/or hints would help me a lot! Many thanks in advance
