How Grid Count Affects Margin Usage and Capital Utilization

Increasing the number of grids raises margin usage roughly in proportion, but it does not increase capital utilization. Capital utilization is mainly determined by the leverage multiplier — the grid count only splits the same amount of capital into finer pieces.
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Two terms first: margin usage is the capital the bot locks up in advance to place and hold orders; capital utilization is the share of your invested capital that is actually working in open orders or positions, rather than sitting idle.
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The more grids you set, the more buy and sell orders the bot needs to place at the same time, so the margin used rises roughly linearly with the grid count — double the number of grids, and the margin used roughly doubles too.
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The reason is that exchanges set a minimum order size for each grid — for example, BTC contracts require at least 0.0001 BTC per grid. The more grids you have, the more times you need to meet this minimum, so the minimum required investment rises accordingly. This is why increasing the grid count often pushes the minimum investment up by more than expected.
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Exchanges also cap the total position size for a single bot. The more grids you have and the larger the total position, the sooner you'll hit this cap, at which point you'll see a prompt like "you can add at most XX U more."
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Capital utilization is mainly determined by the leverage multiplier. As long as the invested capital is sufficient, the bot allocates it proportionally across the grids — the grid count just slices the same capital more finely, without raising or lowering utilization.
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One exception: each grid's order size can only be an integer multiple of the minimum order size — it can't be adjusted continuously. If the capital you add isn't enough to reach the next integer multiple, the extra amount is temporarily held as idle margin, and only gets put to use once you add enough to cross the next threshold. The more grids you have, the higher this threshold tends to be, so it's more common for capital to get stuck between thresholds and sit idle — this is why adding funds sometimes doesn't visibly change your position size or liquidation price.