Do I need a separate grinder for filter and espresso?
No, one good grinder can do both, but you will re-dial every time you switch and you will give something up at one end. Buy separate grinders only when you brew both styles daily and the switching cost genuinely annoys you.
The technical obstacle is not the coarse end, it is the fine end. Espresso needs very fine grinding with very small, repeatable increments, because a quarter turn separates a sour shot from a choked one. Plenty of grinders that are excellent for filter cannot dial in tightly enough down there, or their steps are too coarse to land between gushing and stalling.
So a genuine do-it-all grinder needs stepless or very finely stepped adjustment, burrs that stay consistent when pushed fine, and enough range to reach a French press coarseness without disassembly. Grinders that meet that description exist across a wide range of prices. What they cannot do is be optimal at both: burr geometry that flatters espresso body is not the geometry that flatters pour-over clarity.
The practical annoyance is switching. Moving from an espresso setting to a filter setting and back means re-dialing each time, purging the burr chamber so yesterday's espresso fines do not end up in your V60, and remembering two settings per coffee. With a stepless collar and no reference marks, that is genuinely tedious. Some people solve it with a marked dial or a second adjustment ring.
Decide by your actual split, not your aspirational one. If you are 90 percent filter and occasionally curious about espresso, buy a strong filter grinder that happens to reach espresso and accept that espresso will be a project. If you pull shots every morning and brew filter at weekends, buy espresso-first and accept slightly less clarity in the V60, which most people will not notice.
The two-grinder answer becomes right when both styles are daily rituals, and it is cheaper than it sounds because a good manual grinder handles the filter side beautifully for modest money. A dedicated electric for espresso plus a hand grinder for pour-over is a very common and very sane end state.