Do support gems have attribute requirements in Path of Exile 2?

No: support gems have no attribute requirement (Path of Building's rule, and the game's gem tooltips).

Gem Attribute Requirements

Strength, Dexterity and Intelligence for every gem level · Path of Exile 2✓ Checked against game files · 0.5.5

One attribute, gem level 20

157

e.g. Fireball: Int

75% share, gem level 20

122

of that attribute

50% share, gem level 20

each of two attributes

25% share, gem level 20

of that attribute

A skill gem's attribute requirement grows with the character level its gem level needs. At gem level 20 (character level 90) a single-attribute gem needs 157 Strength, Dexterity or Intelligence; a two-attribute gem needs 86 of each. Support gems need none. Without gear, a class starting with 15 in that attribute needs 29 "+5 to any Attribute" passives to reach 157. Patch 0.5.5, from the game files.

Requirement at every gem level

Gem level	Character level	100%	75%	50%	25%
1	1	—	—	—	—
2	3	9	8	—	—
3	6	14	12	9	—
4	10	21	17	13	9
5	14	28	22	17	11
6	18	35	28	20	13
7	22	41	33	24	15
8	26	48	38	28	17
9	31	57	45	32	19
10	36	65	51	37	22
11	41	74	58	41	24
12	46	82	64	46	26
13	52	92	72	51	29
14	58	103	80	57	32
15	64	113	88	62	35
16	66	116	91	64	36
17	72	126	98	70	39
18	78	137	106	75	42
19	84	147	114	80	45
20	90	157	122	86	48

Share = the gem's split of its requirement (100% Int for Fireball; 50% Dex / 50% Int for Charged Staff). Each gem page shows its own numbers in its level table.

"+5 to any Attribute" passives each class needs for a level 20 gem

Class (base Str/Dex/Int)	Str gem	Dex gem	Int gem
Ranger7/15/7	30	29	30
Huntress7/15/7	30	29	30
Warrior15/7/7	29	30	30
Mercenary11/11/7	30	30	30
Druid11/7/11	30	30	30
Witch7/7/15	30	30	29
Sorceress7/7/15	30	30	29
Monk7/11/11	30	30	30

Passives to reach 157 from the class's starting attribute with the tree's attribute nodes alone; gear, small "+X to Strength" nodes and runes lower it.

How it is worked out

The game files give each gem's attribute split and the character level of each gem level (SkillGems, ItemExperiencePerLevel). The requirement is round((5 + (character level − 3) × 1.7) × (share/100)^0.9) + 4, and none below 8 — Path of Building for PoE2's formula (CalcTools.lua), which matches poe2db's tables (Fireball 157 Int, Charged Staff 86/86 at gem level 20).

Assumptions

The common gem level curve (most skill gems); a gem page uses that gem's own levels.
Requirements under 8 are shown as none, as in Path of Building; poe2db prints them (4 at gem level 1).
Class starting attributes from the game files (Characters).

Gem level	Character level	100%	75%	50%	25%
1	1	—	—	—	—
2	3	9	8	—	—
3	6	14	12	9	—
4	10	21	17	13	9
5	14	28	22	17	11
6	18	35	28	20	13
7	22	41	33	24	15
8	26	48	38	28	17
9	31	57	45	32	19
10	36	65	51	37	22
11	41	74	58	41	24
12	46	82	64	46	26
13	52	92	72	51	29
14	58	103	80	57	32
15	64	113	88	62	35
16	66	116	91	64	36
17	72	126	98	70	39
18	78	137	106	75	42
19	84	147	114	80	45
20	90	157	122	86	48

Gem level	Character level	100%	75%	50%	25%
1	1	—	—	—	—
2	3	9	8	—	—
3	6	14	12	9	—
4	10	21	17	13	9
5	14	28	22	17	11
6	18	35	28	20	13
7	22	41	33	24	15
8	26	48	38	28	17
9	31	57	45	32	19
10	36	65	51	37	22
11	41	74	58	41	24
12	46	82	64	46	26
13	52	92	72	51	29
14	58	103	80	57	32
15	64	113	88	62	35
16	66	116	91	64	36
17	72	126	98	70	39
18	78	137	106	75	42
19	84	147	114	80	45
20	90	157	122	86	48

Gem level	Character level	100%	75%	50%	25%
1	1	—	—	—	—
2	3	9	8	—	—
3	6	14	12	9	—
4	10	21	17	13	9
5	14	28	22	17	11
6	18	35	28	20	13
7	22	41	33	24	15
8	26	48	38	28	17
9	31	57	45	32	19
10	36	65	51	37	22
11	41	74	58	41	24
12	46	82	64	46	26
13	52	92	72	51	29
14	58	103	80	57	32
15	64	113	88	62	35
16	66	116	91	64	36
17	72	126	98	70	39
18	78	137	106	75	42
19	84	147	114	80	45
20	90	157	122	86	48