Is there any word or phrase I can use for Pyrrhic Victory, or perhaps empty
victory, or both? The first being a case where one wins but suffers such huge
damage in some other way that it's victory in name only. The second being a
victory but a generally meaningless one.

"Win the battle, lose the war" might come close.

In lieu of any of the above, a pattern for X "in name only" might suffice.
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phrases yoji-jukugo
What phrase or yojijukugo can I use for Pyrrhic Victory?
You could use the borrowed term ピュロスの勝利 (ピュロス is Pyrrhus!) - this isn't all
that used (3k Google hits on the exact phrase), but it's clearly a concept.

If you wanted to use non-loan words, the definitions for ピュロスの勝利 are usually
given by 割に合わない勝利 or 割りに合わぬ勝利, meaning “a victory that isn’t worth it”. This
likewise isn't a commonly-used phrase in itself, but it expresses what you
want without requiring the audience to know the name Pyrrhus or the history
associated with it.

Moving towards perhaps something more widely used, and closer to your the case
of an "empty victory", I think むなしい勝利 works well. (146k Google hits on the
exact phrase).
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労而無功（労{ろう}して功{こう}なし、労多{ろうおお}くして功少{こうすく}なし） came up to me.

Not 四字熟語{よじじゅくご} though,I think 骨折{ほねお}り損{ぞん}のくたびれ儲{もう}け is similar
expression.

I thought 四字熟語{よじじゅくご} only, otherwise I often use
勝{か}つには勝{か}ったけど、失{うしな}ったものも多{おお}い.

I guess 首{くび}の皮一枚{かわいちまい}でつながる or 命{いのち}からがら帰還{きかん}する also work.
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A few things that I've found along the way that might be related are:

名ばかり e.g. 名ばかりの勝利 i.e. "a victory in name only"

犠牲が多くて引き合わない勝利 - "many sacrifices but unprofitable victory"

損害が大きく得るものが少ない勝利 - "much loss but few gains victory"

And one that's similar, though not identical (but I did mention it above):

武勇戦{ぶゆうせん}に負けて軍略戦{ぐんりゃくせん}で勝つ - directly "lose the bravery battle but win the
strategy battle", and weblio translation: "losing the soldier's war but
winning the general's war"
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