Can I search for a user who has not bought any games?

I want to play Path of Exile with my sister, so she signed up for a Steam Account. However, Path of Exile is a free game and when she tried to add friends she got a message stating she cannot yet add friends. Due to spam protection, she must spend at least $5 on games before she is allowed to invite.

So I figured I'd invite her from my account which does have purchased games, but if I search for her username or email I cannot find her. It seems as if her account isn't visible for some reason. (Possibly because she spent no money? Although that doesn't seem like a "prevent spam/phishing" then, and more like a "must spend money to use this free platform")

Is there a way for me to find her to add her account without her having to spend money on games to lift the limited user restrictions to do the process backwards (invite me; send me a friend request)?

Solution 1:

Based on what everyone else is saying:

Before trying anything, ensure the following:

1. Your sister has logged in at least once (web or client, does not matter)
2. Your sister's profile is set to public (should be by default)

If you are unable to find your sister's account through searching, try asking her to give you her community profile link, since all accounts are allowed to have a profile.

You can find the link by asking her to click on her own name (at the bottom corner of the Steam Client) and copying the link given at the top to you.

Note: If a link does not appear at the top, enable web-friendly links by going to Steam > Settings > Interface and check Display a Steam URL address when available.

Regardless of having a profile created or not, there'll still be a "Add Friend" button, followed by a message in red asking you to encourage the "friend" to create a profile, if one hasn't been set up yet. This also applies to Private accounts where instead of asking you to ask your friend to setup a profile, it simply gives a "This profile is private." message. (And the "Add Friend" button.)

These examples have been created with this account.

Based on your title:

The Steam Limited account restrictions (as far as I can recall) have been around since before 2012. The recent update was only simply a rule change.
Previously, you only needed to activate a CD key or make any purchase to lift the restrictions. Now, you have to spend a minimum of $5USD.

Anyway, a limited account can do the following:

• Receive friend invites and accept/decline them
• Receive voice chat invitations
• Participate in a group chat (if added into one)
• Can view Greenlight, Steam Reviews and Workshop Items
• Subscribe to workshop items if they own the game
• View the Steam Market
• View cards and sets they have crafted (but the level lock still applies)
• Post in the Steam Discussions (with a limit of several posts per 24 hour period)
• Take screenshots and sharing them with friends
• Join and view groups (unless it is private)
• Have a Steam community profile and apply any backgrounds
• Can use emoticons (if they have any)

But it cannot do the following:

• Sending friend invites
• Voice call someone else (they have to be called)
• Opening group chat
• Voting on Greenlight, Steam Reviews and Workshop items
• Participating in the Steam Market
• Posting frequently in the Steam Discussions
• Gaining Steam Profile Levels (Locked to level 0) and Trading Cards
• Submitting content on the Steam Workshop
• Posting in an item's Steam Workshop Discussions
• Accessing the Steam Web API
• Using browser and mobile chat
• Adding public artwork and screenshots

So, if you haven't already deduced...
The only way you can connect with your sister's limited account is for you to send the friend invite itself.

As far as I know, there are no trading restrictions on a new account.
Except for the usual TF2 thing where item drops are non-tradable until upgraded to a Premium Account or (and not a standard Steam Account).

Solution 2:

Your sister is currently a Limited User because, as you said, she has not spent 5USD though Valve's systems.

While she can't send a friend request, you should be able to send her a friend request:

How do I add friends as a limited user?

As a limited user your account is restricted from adding friends. However, you can still accept friend invites from other non-limited users. For example, if a friend is already on Steam and has spent $5 USD or more from the Steam store, they will be able to add you as a friend from your Steam Community profile. You may then accept their friend invite from your Steam account. (emphasis mine)

If you can't find this user through normal add a friend search (which seems to be a weird restriction by Valve), access their profile directly.

To do that you need their profile url, and for their profile to be public (at least until you are friends).

The easiest way to get her profile url is to open Steam, click on her avatar in the bottom right corner, right click on the profile page content itself (since it's really a big web browser) and select "Copy Page URL":

She can then share that url with you though your preferred methods, you can visit that url though a normal web browser, login, and you should be able to send a friend request.