[Although I do use the search, I'm terrible in finding already posted bugs, so please forgive me if I overlooked it.]
Particle effects do show behind or inside glass blocks or glass panes that are being held by an ArmorStand, but only if it's only 1 of them.
If you for example "circle" ArmorStands with e.g. glass panes, the particle effect cannot be seen from the outside, only when you go inside that ArmorStand creation, then you can see the particle effect.
Example pictures are attached.
To make it easier for you to reproduce, I created a one-click stacked command of such a circled panes creation that also automatically sets a repeating CommandBlock with a particle effect.
The one single ArmorStand that gets targetted by the particle effect is visible on purpose.
Insert this stacked command into a regular (Impulse) CommandBlock and trigger it:
/summon FallingSand ~ ~1.5 ~ {Motion:[0.0d,-1.0d,0.0d],Time:1,DropItem:0,Block:redstone_block,Passengers:[
{id:FallingSand,Time:1,DropItem:0,Block:activator_rail},
{id:MinecartCommandBlock,Command:summon ArmorStand ~ ~ ~ {Invisible:1,NoGravity:1,Rotation:[0f,0.0f],ArmorItems:[{},{},{},{id:stained_glass_pane,Damage:5,Count:1}]}},
{id:MinecartCommandBlock,Command:summon ArmorStand ~ ~ ~ {Invisible:1,NoGravity:1,Rotation:[22.5f,0.0f],ArmorItems:[{},{},{},{id:stained_glass_pane,Damage:5,Count:1}]}},
{id:MinecartCommandBlock,Command:summon ArmorStand ~ ~ ~ {Invisible:1,NoGravity:1,Rotation:[45f,0.0f],ArmorItems:[{},{},{},{id:stained_glass_pane,Damage:5,Count:1}]}},
{id:MinecartCommandBlock,Command:summon ArmorStand ~ ~ ~ {Invisible:1,NoGravity:1,Rotation:[67.5f,0.0f],ArmorItems:[{},{},{},{id:stained_glass_pane,Damage:5,Count:1}]}},
{id:MinecartCommandBlock,Command:summon ArmorStand ~ ~ ~ {Invisible:1,NoGravity:1,Rotation:[90f,0.0f],ArmorItems:[{},{},{},{id:stained_glass_pane,Damage:5,Count:1}]}},
{id:MinecartCommandBlock,Command:summon ArmorStand ~ ~ ~ {Invisible:1,NoGravity:1,Rotation:[112.5f,0.0f],ArmorItems:[{},{},{},{id:stained_glass_pane,Damage:5,Count:1}]}},
{id:MinecartCommandBlock,Command:summon ArmorStand ~ ~ ~ {Invisible:1,NoGravity:1,Rotation:[135f,0.0f],ArmorItems:[{},{},{},{id:stained_glass_pane,Damage:5,Count:1}]}},
{id:MinecartCommandBlock,Command:summon ArmorStand ~ ~ ~ {Invisible:1,NoGravity:1,Rotation:[157.5f,0.0f],ArmorItems:[{},{},{},{id:stained_glass_pane,Damage:5,Count:1}]}},
{id:MinecartCommandBlock,Command:summon ArmorStand ~ ~ ~ {Invisible:1,NoGravity:1,Rotation:[180f,0.0f],ArmorItems:[{},{},{},{id:stained_glass_pane,Damage:5,Count:1}]}},
{id:MinecartCommandBlock,Command:summon ArmorStand ~ ~ ~ {Invisible:1,NoGravity:1,Rotation:[202.5f,0.0f],ArmorItems:[{},{},{},{id:stained_glass_pane,Damage:5,Count:1}]}},
{id:MinecartCommandBlock,Command:summon ArmorStand ~ ~ ~ {Invisible:1,NoGravity:1,Rotation:[225f,0.0f],ArmorItems:[{},{},{},{id:stained_glass_pane,Damage:5,Count:1}]}},
{id:MinecartCommandBlock,Command:summon ArmorStand ~ ~ ~ {Invisible:1,NoGravity:1,Rotation:[247.5f,0.0f],ArmorItems:[{},{},{},{id:stained_glass_pane,Damage:5,Count:1}]}},
{id:MinecartCommandBlock,Command:summon ArmorStand ~ ~ ~ {Invisible:1,NoGravity:1,Rotation:[270f,0.0f],ArmorItems:[{},{},{},{id:stained_glass_pane,Damage:5,Count:1}]}},
{id:MinecartCommandBlock,Command:summon ArmorStand ~ ~ ~ {Invisible:1,NoGravity:1,Rotation:[292.5f,0.0f],ArmorItems:[{},{},{},{id:stained_glass_pane,Damage:5,Count:1}]}},
{id:MinecartCommandBlock,Command:summon ArmorStand ~ ~ ~ {Invisible:1,NoGravity:1,Rotation:[315f,0.0f],ArmorItems:[{},{},{},{id:stained_glass_pane,Damage:5,Count:1}]}},
{id:MinecartCommandBlock,Command:summon ArmorStand ~ ~ ~ {Invisible:1,NoGravity:1,Rotation:[337.5f,0.0f],ArmorItems:[{},{},{},{id:stained_glass_pane,Damage:5,Count:1}]}},
{id:MinecartCommandBlock,Command:"summon ArmorStand ~ ~1 ~ {Tags:[\"AS\"],NoGravity:1}"},
{id:MinecartCommandBlock,Command:"setblock ~ ~-2 ~1 minecraft:repeating_command_block 0 replace {auto:1b,Command:\"execute @e[tag=AS] ~ ~ ~ particle reddust ~ ~1 ~ 0.01 1 0 1\",TrackOutput:0}"},
{id:MinecartCommandBlock,Command:setblock ~ ~-2 ~ command_block 0 replace {SuccessCount:0b,auto:1b,Command:fill ~ ~ ~ ~ ~2 ~ air}},
{id:MinecartCommandBlock,Command:kill @e[type=MinecartCommandBlock,r=0]}
]}
I'll conduct some more tests, but if you know already what exact examples or commands you need to narrow down the issue, please let me know.
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This is most probably MC-9553

Thank you, I'll add the command and pictures there then! 😸
This issue can then be closed as duplicate, I guess.
Chill holidays }=)